Download - COMPOUND INTEREST
SME–539
COMPOUND INTEREST
Importance : In examinations of different levels 1 or2 questions of compound interest are essentially asked,they differ in difficulty level. Questions are of limitedvariety and hence, marks may be ensured withpreparation.
Scope of questions : Questions asked in differentexaminations are mainly of two types – Based oncompound interest only and based on both of simpleinterest and compound interest. Rate of interest may beyearly, half yearly or quarterly. EMI (Equal MonthlyInstallments) based questions are also asked.
Way to success : Questions can be solved easily bylearning basic concepts and formulae learning squaresand cubes of numbers will increase speed.
RULE 1 : If A = Amount, P = Principal, r = Rate ofCompound Interest (C.I.), n = no. of years then,
A = Pr n
1100
+FHG
IKJ , C.I. = A – P
C.I. = P 1100
1+FHG
IKJ -
LNMM
OQPP
r n
RULE 2 : Compound interest is calculated on four basis:Rate Time(n)
Annually r% t years
Half–yearlyr2
% t × 2 years
(Semi-annually)
Quarterlyr4
% t × 4 years
Monthlyr
12% t × 12 years
RULE 3 : If there are distinct ‘rates of interest’ fordistinct time periods i.e.,
Rate for 1st year ® r1%Rate for 2nd year ® r2 %Rate for 3rd year ® r3 % and so on
Then A = P 1100
1100
1100
1 2 3+FHG
IKJ +FHG
IKJ +FHG
IKJ
r r r............
C.I. = A – PRULE 4 : If the time is in fractional form i.e.,t = nF, then
A = P 1100
+FHG
IKJ
r n1
100+F
HGIKJ
rFe.g. t = 3
57
yrs, then
A = P 1100
3
+FHG
IKJ
r 1100
57
+ ´FHG
IKJ
r
RULE 5 : A certain sum becomes ‘m’ times of itself in ‘t’years on compound interest then the time it will take tobecome mn times of itself is t × n years.
COMPOUND INTEREST
RULE 6 : The difference between C.I. and S.I. on asum ‘P’ in 2 years at the rate of R% rate of compoundinterest will be
C.I – S.I. = PR
100
2FHG
IKJ =
S I R. .´200
For 3 years, C.I. – S.I. = PR
100
2FHG
IKJ ´ +F
HGIKJ3
100R
RULE 7 : If on compound interest, a sum becomes Ain ‘a’ years and B in ‘b’ years then,
(i) If b – a = 1, then, R% =BA
-FHG
IKJ ´1 100%
(ii) If b – a = 2, then, R% =BA
-FHG
IKJ ´1 100%
(iii) If b – a = n then, R% =BA
nFHG
IKJ -
L
NMMM
O
QPPP
´
1
1 100%
where n is a whole number.RULE 8 : If a sum becomes ‘n’ times of itself in ‘t’ years
on compound interest, then R% = n t1
1 100%-LNMM
OQPP ´
RULE 9 : If a sum ‘P’ is borrowed at r% annualcompound interest which is to be paid in ‘n’ equal annualinstallments including interest, then
(i) for n = 2, Each annual installment
=
P
r r100
100100
100
2
+FHG
IKJ +
+FHG
IKJ
(ii) For n = 3, Each annual installment
=
P
r r r100
100100
100100
100
2 3
+FHG
IKJ +
+FHG
IKJ +
+FHG
IKJ
RULE 10 : The simple interest for a certain sum for 2years at an annual rate interest R% is S.I., then
C.I. = S.I. 1200
+FHG
IKJ
R
RULE 11 : A certain sum at C.I. becomes x times in n1
year and y times in n2 years thenxn
1
1= y n
1
2
qqq
11
SME–540
COMPOUND INTEREST
TYPE–I
1. At what percent per annum will3000/- amounts to 3993/-
in 3 years if the interest is com-pounded annually?(1) 9% (2) 10%(3) 11% (4) 13%(SSC CGL Prelim Exam. 27.02.2000
(First Sitting) & (SSC SAS Exam.26.06.2010 (Paper-I)
2. The compound interest on10,000 in 2 years at 4% perannum, the interest beingcompounded half-yearly, is :(1) 636.80 (2) 824.32(3) 912. 86 (4) 828. 82(SSC CGL Prelim Exam. 27.02.2000
(Second Sitting)
3. In how many years will 2,000amounts to 2,420 at 10% perannum compound interest?
(1) 3 years (2) 2 12 years
(3) 2 years (4) 112 years
(SSC CGL Prelim Exam. 27.02.2000(IInd Sitting & (SSC CGL PrelimExam. 13.11.2005 (IInd Sitting)
4. In what time will 1000 becomes 1331 at 10% per annum com-
pounded annually ?
(1) 3 years (2) 212
years
(3) 2 years (4) 312
years
(SSC CGL Prelim Exam. 08.02.2004(Second Sitting) & (SSC MTS
Exam-. 24.03.2013 (Ist Sitting)5. The principal, which will amount
to 270.40 in 2 years at the rateof 4% per annum compound in-terest, is(1) 200 (2) 225(3) 250 (4) 220
(SSC CPO S.I. Exam. 05.09.2004)6. A sum of money on compound
interest amounts to 10648 in 3years and 9680 in 2 years. Therate of interest per annum is :(1) 5% (2) 10%(3) 15% (4) 20%
(SSC CPO S.I. Exam. 26.05.2005)
7. At what rate per cent per annumwill 2304 amount to 2500 in2 years at compound interest ?
(1) 412
% (2) 415
%
(3) 416
% (4) 413
%
(SSC CPO S.I. Exam. 05.09.2004)& (SSC CGL Prelim Exam.13.11.2005 (First Sitting)
8. A sum becomes 1,352 in 2years at 4% per annum com-pound interest. The sum is(1) 1,225 (2) 1,270(3) 1,245 (4) 1,250(SSC CGL Prelim Exam. 11.05.2003
(IInd Sitting) & (SSC CGL PrelimExam. 13.11.2005 (IInd Sitting) &(SSC CISF ASI Exam. 29.08.2010)
9. The compound interest on16,000 for 9 months at 20%
per annum, interest being com-pounded quarterly, is(1) 2,520 (2) 2,524(3) 2,522 (4) 2,518
(SSC CPO S.I. Exam. 03.09.2006)
10. If the rate of interest be 4% perannum for first year, 5% per an-num for second year and 6% perannum for third year, then thecompound interest of 10,000for 3 years will be(1) 1,600 (2) 1,625.80(3) 1,575.20 (4) 2,000
(SSC CPO S.I. Exam. 03.09.2006)
11. The compound interest on 2000in 2 years if the rate of interestis 4% per annum for the firstyear and 3% per annum for thesecond year, will be(1) 142.40 (2) 140.40(3) 141.40 (4) 143.40(SSC CGL Prelim Exam. 04.02.2007
(Second Sitting)
12. At what rate per annum will 32000 yield a compound interest
of 5044 in 9 months interestbeing compounded quarterly ?(1) 20% (2) 32%(3) 50% (4) 80%(SSC CGL Prelim Exam. 04.02.2007
(Second Sitting)
13. The compound interest on 8,000at 15% per annum for 2 years 4months, compounded annually is:
(1) 2980 (2) 3091(3) 3109 (4) 3100
(SSC CPO S.I. Exam. 16.12.2007)14. In what time will 10,000
amount to 13310 at 20% perannum compounded half yearly?
(1) 112
years (2) 2 years
(3) 212
years (4) 3 years
(SSC CGL Prelim Exam. 27.07.2008(First Sitting)
15. A certain sum of money yields1261 as compound interest for 3years at 5% per annum. The sum is(1) 9000 (2) 8400(3) 7500 (4) 8000(SSC CGL Prelim Exam. 27.07.2008
(First Sitting)16. A certain sum, invested at 4% per
annum compound interest,compounded halfyearly, amountsto 7,803 at the end of one year..The sum is(1) 7,000 (2) 7,200(3) 7,500 (4) 7,700
(SSC CGL PrelimExam. 27.07.2008 (IInd Sitting)
17. A certain sum amounts to 5,832in 2 years at 8% per annum com-pound interest, the sum is(1) 5,000 (2) 5,200(3) 5,280 (4) 5,400(SSC CGL Prelim Exam. 27.07.2008
(Second Sitting)18. The compound interest on
6,000 at 10% per annum for
1 12 years, when the interest be-
ing compounded annually, is(1) 910 (2) 870(3) 930 (4) 900
(SSC CPO S.I. Exam. 09.11.2008)19 In what time 8,000 will amount
to 9,261 at 10% per annum com-pound interest, when the inter-est is compounded half yearly ?
(1) 312
years (2) 112
years
(3) 212
years (4) 2 years
(SSC CPO S.I. Exam. 09.11.2008)
QUESTIONS ASKED IN PREVIOUS SSC EXAMS
SME–541
COMPOUND INTEREST
20. At what rate per cent per annumwill a sum of 1,000 amounts to 1,102.50 in 2 years at com-
pound interest ?(1) 5% (2) 5.5%(3) 6% (4) 6.5%(SSC CGL Tier-I Exam. 16.05.2010
(First Sitting)21. In how many years will a sum of
800 at 10% per annum com-pound interest, compoundedsemi-annually becomes 926.10 ?
(1) 112
years (2) 123
years
(3) 213
years (4) 212
years
(SSC CGL Tier-I Exam. 16.05.2010(Second Sitting)
22. An amount of 6,000 lent at 5%per annum compound interest for2 years will become(1) 600 (2) 6,600(3) 6,610 (4) 6,615
(SSC (South Zone) InvestigatorExam. 12.09.2010)
23. In what time will 1000 amountsto 1331 at 20% per annum,compounded half yearly ?
(1) 112
years (2) 2 years
(3) 1 year (4) 212
years
(SSC CGL Prelim Exam. 11.05.2003(First Sitting)
24. The compound interest on30,000 at 7% per annum for a
certain time is 4,347. Thetime is(1) 3 years (2) 4 years(3) 2 years (4) 2.5 years
(SSC Sub-Inspector & LDC Exam.21.10.2012 (Ist Sitting)
25. A sum of 8000 will amount to 8820 in 2 years if the interest
is calculated every year. The rateof compound interest is(1) 6% (2) 7%(3) 3% (4) 5%(SSC Sub-Inspector & LDC Exam.
28.10.2012, Ist Sitting)26. A principal of 10,000, after 2
years compounded annually, therate of interest being 10% perannum during the first year and12% per annum during the sec-ond year (in rupees) will amountto :
(1) 12,000 (2) 12,320(3) 12,500 (4) 11,320(SSC Sub-Inspector & LDC Exam.
04.11.2012, Ist Sitting)
27. The sum of money that yields acompound interest of 420 dur--ing the second year at 5% p.a is
(1) 4,000 (2) 42,000
(3) 8,000 (4) 21,000(SSC Graduate Level Tier-I
Exam. 11.11.2012, Ist Sitting)
28. A man saves 2000 at the endof each year and invests themoney at 5% compound inter-est. At the end of 3 years hewill have :(1) 4305 (2) 6305(3) 4205 (4) 2205
(SSC Multi-Tasking StaffExam. 10.03.2013)
29. The time in which 80,000amounts to 92,610 at 10%p.a. compound interest, inter-est being compounded semiannually is :
(1) 112
years (2) 2 years
(3) 212
years (4) 3 years
(SSC Graduate Level Tier-IExam. 21.04.2013, Ist Sitting)
30. A man borrows 21000 at 10%compound interest. How muchhe has to pay annually at theend of each year, to settle hisloan in two years ?(1) 12000 (2) 12100(3) 12200 (4) 12300
(SSC Graduate Level Tier-IExam. 21.04.2013 IInd Sitting)
31. 800 at 5% per annum com-pounded annually will amountto 882 in(1) 1 year (2) 2 years(3) 3 years (4) 4 years
(SSC Constable (GD)Exam. 12.05.2013)
32. The compound interest on5,000 for 3 years at 10% p. a.will amount to(1) 1,654 (2) 1,655(3) 1,600 (4) 1,565
(SSC Graduate Level Tier-IIExam. 29.09.2013)
33. A sum of 3,200 invested at 10%p.a. compounded quarterlyamounts to 3,362. Compute thetime period.
(1)12
year (2) 1 year
(3) 2 years (4)34
year
(SSC Graduate Level Tier-IIExam. 29.09.2013)
34. The compound interest on a cer-tain sum of money for 2 years at5% is 328, then the sum is(1) 3000 (2) 3600(3) 3200 (4) 3400(SSC CGL Tier-II Exam. 21.09.2014)
35. Two years ago, the value of mymotorbike was 62500. If thevalue depreciates by 4% everyyear, now its value is(1) 56700 (2) 57600(3) 57500 (4) 55700(SSC CGL Tier-II Exam. 21.09.2014)
36. The compound interest on a sumof money for 2 years is 615and the simple interest for thesame period is 600. Find theprincipal.
(1) 6,500 (2) 6,000(3) 8,000 (4) 9,500(SSC CHSL DEO Exam. 16.11.2014)
(Ist Sitting)
37. Rekha invested a sum of 12000 at 5% per annum com-
pound interest. She received anamount of 13230 after n years.Find n.(1) 2.8 years (2) 3.0 years(3) 2.5 years (4) 2.0 years
(SSC CAPFs SI, CISF ASI & DelhiPolice SI Exam. 22.06.2014
TF No. 999 KP0)38. When principal = S, rate of
interest = 2r % p.a, then a per-son will get after 3 years at com-pound interest
(1)6Sr100
(2) S 1+r
100FHG
IKJ3
(3) S 1+r
50FHG
IKJ3
(4) 3S 1+r
100FHG
IKJ3
(SSC CGL Tier-II Exam. 12.04.2015TF No. 567 TL 9)
SME–542
COMPOUND INTEREST
39. The sum of money which be-comes 2420 at 10 % rate ofcompound interest after twoyears is(1) 2000 (2) 1000
(3) 2500 (4) 1500(SSC CGL Tier-II Exam. 12.04.2015
TF No. 567 TL 9)
40. On a certain principal the com-pound interest compounded an-nually for the second year at 10%per annum is 132. The prin-cipal is(1) 1250 (2) 1000(3) 1200 (4) 1320(SSC CGL Tier-II Exam. 12.04.2015
TF No. 567 TL 9)
41. The principal that yields a com-pound interest of Rs. 420 duringthe second year at 5% per an-num is
(1) Rs. 7,000 (2) Rs. 5,000
(3) Rs. 8,000 (4) Rs. 6,000(SSC CGL Tier-II Exam,
2014 12.04.2015 (Kolkata Region)TF No. 789 TH 7)
42. In what time will Rs. 64,000amount to Rs. 68,921 at 5% perannum, interest being compound-ed half yearly ?
(1) 3 years (2) 212
years
(3) 2 years (4) 112
years
(SSC CAPFs SI, CISF ASI & DelhiPolice SI Exam, 21.06.2015
IInd Sitting)
43. A certain sum will amount to12,100 in 2 years at 10% perannum of compound interest, in-terest being compounded annu-ally. The sum is(1) 8000 (2) 6000(3) 12000 (4) 10000(SSC CGL Tier-I Exam, 16.08.2015
(Ist Sitting) TF No. 3196279)
44. At what rate of compound inter-est per annum will a sum of Rs.1200 become Rs. 1348.32 in 2years?(1) 7.5% (2) 6.5%(3) 7% (4) 6%
(SSC CHSL (10+2) LDC, DEO& PA/SA Exam, 15.11.2015(IInd Sitting) TF No. 7203752)
45. The compound interest on Rs.12000 for 9 months at 20% perannum, interest being compound-ed quarterly is :
(1) Rs. 1750 (2) Rs. 2089-70(3) Rs. 1891-50 (4) Rs. 2136-40
(SSC CHSL (10+2) LDC, DEO& PA/SA Exam, 06.12.2015
(IInd Sitting) TF No. 3441135)46. The compound interest on Rs.
30,000 at 7% per annum for nyears is Rs. 4347. The value of nis(1) 3 (2) 2(3) 4 (4) 5
(SSC CGL Tier-II OnlineExam.01.12.2016)
47. A sum of Rs. 2420 is accumulat-ed in 2 years at 10% compundinterest on a certain amount. Thenthe original amount is :(1) Rs. 1000 (2) Rs. 2000(3) Rs. 1500 (3) Rs. 2500
(SSC CPO Exam. 06.06.2016) (Ist Sitting)
48. The compound interest on a sumof Rs. 5000 at 8% per annum for9 months when interest is com-pound quarterly is :(1) Rs. 300 (2) Rs. 300.12(3) Rs. 306.04 (4) Rs. 308
(SSC CAPFs (CPO) SI & ASI,Delhi Police Exam. 05.06.2016)
(Ist Sitting)49. A sum of money invested at com-
pound interest amounts to Rs.800 in 3 years and to Rs. 840 in4 years. The rate of interest perannum is :
(1) 212
% (2) 4%
(3) 5% (4) 623
%
(SSC CGL Tier-I (CBE)Exam. 27.08.2016) (IInd Sitting)
50. In how many years will a sum ofRs. 800 at 10% per annum com-pounded semi-annually becomeRs. 926.10?
(1) 212
years (2) 3 years
(3) 2 years (4) 112
years
(SSC CGL Tier-I (CBE)Exam. 27.08.2016) (IInd Sitting)
51. A sum of Rs. 2000 amounts toRs. 4000 in two years at com-pound interest. In how manyyears will the same amount be-come Rs. 8000 ?(1) 2 (2) 4(3) 6 (4) 8
(SSC CGL Tier-I (CBE)Exam. 29.08.2016) (IInd Sitting)
52. The compound interest onRs. 64,000 for 3 years, compound-ed annually at 7.5% p.a. is(1) Rs. 14,400 (2) Rs. 15,705(3) Rs. 15,507 (4) Rs. 15,075
(SSC CGL Tier-I (CBE)Exam. 01.09.2016) (Ist Sitting)
53. Find the amount which Shyamwill get on Rs. 4096, if he gives
it for 18 months at 1212
% per
annum, interest being compound-ed half yearly.(1) Rs. 5,813 (2) Rs. 4,515(3) Rs. 4,913 (4) Rs. 5,713
(SSC CGL Tier-I (CBE)Exam. 02.09.2016) (IInd Sitting)
54. If Rs. 10000 amounts to Rs.11664 invested in compound in-terest (compounded annually) fortwo years then the annual rate ofcompound interest is(1) 10% (2) 9%(3) 8% (4) 6%
(SSC CGL Tier-I (CBE)Exam. 06.09.2016) (Ist Sitting)
55. The compound interest on Rs.4000 for 4 years at 10% per an-num will be(1) Rs. 1856.40 (2) Rs. 1600(3) Rs. 1856 (4) Rs. 1756.60
(SSC CGL Tier-II (CBE)Exam. 30.11.2016)
56. A man invested a sum of moneyat compound interest. It amount-ed to Rs. 2420 in 2 years and toRs. 2662 in 3 years. Find thesum.(1) Rs. 1000 (2) Rs. 2000(3) Rs. 5082 (4) Rs. 3000
(SSC CGL Tier-II OnlineExam.01.12.2016)
57. A sum of Rs. 3000 amounts toRs. 6000 in two years at com-pound interest. The interest forfour years is :(1) Rs. 9000 (2) Rs. 12000(3) Rs. 6000 (4) Rs. 3000
(SSC CGL Tier-I (CBE)Exam. 31.08.2016 (IIIrd Sitting)
58. If a sum of Rs.12500 is investedfor 1 year at 12% per annum in-terest being compounded semi-annually, then interest earned is :(1) Rs.1505 (2) Rs.1535(3) Rs.1545 (4) Rs.1550
(SSC CGL Tier-I (CBE)Exam. 06.09.2016 (IInd Sitting)
59. A sum of money amounts to Rs.6655 at the rate of 10% com-pounded annually for 3 years.The sum of money is(1) Rs. 5000 (2) Rs. 5500(3) Rs. 6000 (4) Rs. 6100
(SSC CGL Tier-I (CBE)Exam. 06.09.2016 (IIIrd Sitting)
SME–543
COMPOUND INTEREST
60. In what time (in years) will Rs.8000 amount to Rs. 9261 at 5%per annum, compounded annu-ally?
(1) 3 (2) 312
(3) 4 (4) 412
(SSC CGL Tier-I (CBE)Exam. 07.09.2016 (IIIrd Sitting)
61. The compound interest on Rs.1000 at 10% per annum for 3years in (Rs.) is :(1) Rs. 1331 (2) Rs. 331(3) Rs. 300 (4) Rs. 1300
(SSC CGL Tier-I (CBE)Exam. 08.09.2016 (IInd Sitting)
62. What would be the compoundinterest of Rs. 25000 for 2 yearsat the rate of 5% per annum ?(1) Rs. 2500 (2) Rs. 2562.5(3) Rs. 2425.25 (4) Rs. 5512.5
(SSC CGL Tier-I (CBE)Exam. 09.09.2016 (IInd Sitting)
63. The compound interest on Rs.
24000 at 10% per annum for 112
years, interest being compound-ed semi-annually is :(1) Rs. 3783 (2) Rs. 3777(3) Rs. 3780 (4) Rs. 3781
(SSC CGL Tier-I (CBE)Exam. 09.09.2016 (IIIrd Sitting)
64. The sum for 2 years gives a com-pound interest of Rs. 3225 at therate of 15% per annum. The sumis(1) Rs. 10000 (2) Rs. 20000(3) Rs. 15000 (4) Rs. 32250
(SSC CGL Tier-II (CBE)Exam. 12.01.2017)
65. In 3 years Rs. 3000 amounts toRs. 3993 at x% compound inter-est, compounded annually. Thevalue of x is(1) 10 (2) 8
(3) 5 (4) 313
(SSC CGL Tier-II (CBE)Exam. 12.01.2017)
66. The least number of years inwhich a sum of money on 19%p.a. compound interest will bemore than double is(1) 3 years (2) 4 years(3) 5 years (4) 2 years
(SSC Multi-Tasking StaffExam. 30.04.2017)
TYPE–II
1. If the compound interest on acertain sum for 2 years at 3% perannum is 101.50, then thesimple interest on the same sumat the same rate and for the sametime will be(1) 90.00 (2) 95.50(3) 100.00 (4) 98.25
(SSC CPO S.I. Exam. 12.01.20032. If the compound interest on a
sum of money for 3 years at therate of 5% per annum is252.20, the simple interest onthe same sum at the same rateand for the same time is(1) 220 (2) 240(3) 245 (4) 250
(SSC CPO S.I. Exam. 07.09.2003)3. On a certain sum of money the
compound interest for 2 years is 282.15 and the simple inter--
est for the same period of timeis 270. The rate of interest perannum is(1) 6.07% (2) 10%(3) 9% (4) 12.15%
(SSC CPO S.I. Exam. 07.09.2003)4. If the compound interest on a
sum for 2 years at 1212
% per
annum is 510, the simple in-terest on the same sum at thesame rate for the same period oftime is :(1) 400 (2) 480(3) 450 (4) 460(SSC CGL Prelim Exam. 08.02.2004
(First Sitting)5. The compound interest on a cer-
tain sum of money at a certainrate for 2 years is 40.80 andthe simple interest on the samesum is 40 at the same rate andfor the same time. The rate ofinterest is(1) 2% per annum(2) 3% per annum(3) 4% per annum(4) 5% per annum
(SSC CPO S.I. Exam. 05.09.2004)6. The compound interest on a cer-
tain sum of money invested for2 years at 5% per annum is328. The simple interest on thesum, at the same rate and forthe same period will be(1) 320 (2) 308(3) 300 (4) 287(SSC CPO S.I. Exam. 05.09.2004) &
(SSC CPO S.I. Exam. 26.05.2005)
7. Compound interest on a sum ofmoney for 2 years at 4 per centper annum is 2, 448. Simpleinterest of the same sum of mon-ey at the same rate of interest for2 years will be(1) 2,500 (2) 2,400
(3) 2,360 (4) 2,250
(SSC Section Officer (CommercialAudit) Exam. 26.11.2006
(Second Sitting)
8. At a certain rate per annum, thesimple interest on a sum of mon-ey for one year is 260 and thecompound interest on the samesum for two years is 540.80.The rate of interest per annum is(1) 4% (2) 6%(3) 8% (4) 10%(SSC CGL Prelim Exam. 27.07.2008
(First Sitting)
9. The simple interest on a sum ofmoney at 4% per annum for 2years is 80. The compound in-terest in the same sum for thesame period is(1) 82.60 (2) 82.20(3) 81.80 (4) 81.60(SSC CGL Prelim Exam. 27.07.2008
(First Sitting)
10. The compound interest on a cer-tain sum of money at 5% perannum for 2 years is 246. Thesimple interest on the same sumfor 3 years at 6% per annum is(1) 435 (2) 450(3) 430 (4) 432(SSC CGL Prelim Exam. 27.07.2008
(Second Sitting)
11. The simple interest and compoundinterest (compounded annually)on a certain sum of money with agiven rate for a period of 2 yearsare 900 and 954 respectively.The sum of money is(1) 3700 (2) 3650(3) 3850 (4) 3750
(SSC CPO S.I. Exam. 09.11.2008)
12. The compound interest on a cer-tain sum of money for 2 years at10% per annum is 420. Thesimple interest on the same sumat the same rate and for the sametime will be
(1) 350 (2) 375
(3) 380 (4) 400(SSC Assistant Grade-III Exam.
11.11.2012 (IInd Sitting)
SME–544
COMPOUND INTEREST
13. If the compound interest on acertain sum for 2 years at 4% p.a.is 102, the simple interest atthe same rate of interest for twoyears would be
(1) 200 (2) 50(3) 150 (4) 100
(SSC CGL Exam. 04.07.1999 (IstSitting) & (SSC Multi-Tasking StaffExam. 17.03.2013, Kolkata Region)
14. There is 100% increase to anamount in 8 years, at simple in-terest. Find the compound inter-est of 8000 after 2 years at thesame rate of interest.
(1) 2500 (2) 2000
(3) 2250 (4) 2125(SSC Graduate Level Tier-I
Exam. 21.04.2013)
15. If the compound interest on acertain sum for two years at 12%per annum is 2,544, the sim-ple interest on it at the same ratefor 2 years will be
(1) 2,400 (2) 2,500(3) 2,480 (4) 2,440
(SSC Graduate Level Tier-IExam. 19.05.2013)
16. A sum becomes 2,916 in 2years at 8% per annum com-pound interest. The simple inter-est at 9% per annum for 3 yearson the same amount will be
(1) 600 (2) 675
(3) 650 (4) 625(SSC Sub-Inspector & LDC
Exam. 20.10.2013)
17. The compound interest on a cer-tain sum of money at a certainrate per annum for two years is
2,050, and the simple intereston the same amount of money atthe same rate for 3 years is 3,000. Then the sum of money is
(1) 20,000 (2) 18,000(3) 21,000 (4) 25, 000
(SSC CGL Tier-I Re-Exam. (2013)20.07.2014 (IInd Sitting)
18. The compound interest on a cer-tain sum of money for 2 years at5% per annum is 410. The sim-ple interest on the same sum atthe same rate and for the sametime is
(1) 400 (2) 300(3) 350 (4) 405
(SSC CGL Tier-IExam. 19.10.2014 (Ist Sitting)
19. If the compound interest on a
sum for 2 years at 1212
p.a is
510, the simple interest on thesame sum at the same rate forthe same period of time is(1) 400 (2) 450(3) 460 (4) 480
(SSC CGL Tier-IIExam. 21.09.2014)
20. A man borrowed some moneyfrom a private organisation at 5%simple interest per annum. Helended 50% of this money to an-other person at 10% compoundinterest per annum and therebythe man made a profit of Rs.3,205 in 4 years. The man bor-rowed.(1) Rs. 80,000(2) Rs. 1,00,000(3) Rs. 1,20,000(4) Rs. 1,50,000(SSC CGL Tier-I Exam. 19.10.2014
TF No. 022 MH 3)
21. A certain amount of money earnsRs. 540 as Simple Interest in 3years. If it earns a CompoundInterest of Rs. 376.20 at thesame rate of interest in 2 years,find the amount (in Rupees).(1) 1600 (2) 1800(3) 2000 (4) 2100
(SSC CAPFs SI, CISF ASI & DelhiPolice SI Exam, 21.06.2015
(Ist Sitting) TF No. 8037731)22. On a certain sum of money, the
simple interest for 2 years is Rs.350 at the rate of 4% per annum.If it was invested at compoundinterest at the same rate for thesame duration as before, howmuch more interest would beearned ?(1) Rs. 3.50 (2) Rs. 7(3) Rs. 14 (4) Rs. 35
(SSC CPO Exam. 06.06.2016) (Ist Sitting)
23. The simple interest on a sum ofmoney for 3 years is Rs. 240 andthe compound interest on thesame sum, at the same rate for 2years is Rs. 170. The rate of in-terest is :
(1) 8% (2) 2916
%
(3) 1212
(4) 55
17%
(SSC CAPFs (CPO) SI & ASI,Delhi Police Exam. 20.03.2016)
(IInd Sitting)
24. The simple interest on a certainsum of money for 2 years at 5%is Rs. 1600. The compound in-terest at the same rate after 3years interest compound annu-ally, is(1) Rs.2520 (2) Rs.2522(3) Rs.2555 (4) Rs.2535
(SSC CGL Tier-I (CBE)Exam. 30.08.2016) (Ist Sitting)
25. A man borrowed some moneyfrom a private organisation at 5%simple interest per annum. Helended this money to anotherperson at 10% compound inter-est per annum, and made a prof-it of Rs. 26,410 in 4 years. Theman borrowed(1) Rs. 200000 (2) Rs. 150000(3) Rs. 132050 (4) Rs. 100000
(SSC CGL Tier-I (CBE)Exam. 31.08.2016) (IInd Sitting)
26. If the simple interest on a sum ofmoney for 2 years at 5% per an-num is Rs. 50, the compoundinterest on the same at the samerate and for the same time is :(1) Rs. 50.50 (2) Rs. 51.25(3) Rs. 51.50 (4) Rs. 50.05
(SSC CGL Tier-I (CBE)Exam. 02.09.2016) (IInd Sitting)
27. There is 40% increase in anamount in 8 years at simple in-terest. What will be the com-pound interest (in rupees) of Rs30000 after 2 years at the samerate ?(1) 6150 (2) 7687.5(3) 4612.5 (4) 3075
(SSC CHSL (10+2) Tier-I (CBE)Exam. 16.01.2017) (IInd Sitting)
TYPE–III1. If the difference between the
compound interest, compoundedevery six months, and thesimple interest on a certain sumof money at the rate of 12% perannum for one year is 36, thesum is :(1) 10,000 (2) 12,000(3) 15,000 (4) 9,000(SSC CGL Prelim Exam. 27.02.2000
(Second Sitting)2. What is the difference between
compound interest on 5,000 for
112 years at 4% per annum
according as the interest iscompounded yearly or half-yearly?(1) 2.04 (2) 3.06(3) 8.30 (4) 4.80(SSC CGL Prelim Exam. 27.02.2000
(Second Sitting)
SME–545
COMPOUND INTEREST
16. The difference between compoundand simple interest on a certainsum for 3 years at 5% per annumis Rs. 122. The sum is(1) 16,000 (2) 15,000(3) 12,000 (4) 10,000
(SSC CGL Prelim Exam.27.07.2008 (Second Sitting)
17. The difference between simpleinterest and compound interest ofa certain sum of money at 20%per annum for 2 years is 48.Then the sum is(1) 1,000 (2) 1, 200(3) 1, 500 (4) 2, 000
(SSC CGL Tier-1 Exam.19.06.2011 (First Sitting)
18. The difference between thecompound interest and simpleinterest on 10,000 for 2 yearsis 25. The rate of interest perannum is
(1) 5% (2) 7%
(3) 10% (4) 12%(SSC CGL Tier-1 Exam. 26.06.2011
(First Sitting)19. If the difference between S.I.
and C.I. for 2 years on a sum ofmoney lent at 5% is 6, thenthe sum is(1) 2200 (2) 2400(3) 2600 (4) 2000(SSC CGL Tier-1 Exam. 26.06.2011
(Second Sitting)20. On a certain sum of money lent
out at 16% p.a. the differencebetween the compound interestfor 1 year, payable half yearly,and the simple interest for 1year is 56. The sum is(1) 1080 (2) 7805(3) 8750 (4) 5780
(SSC CPO (SI, ASI & IntelligenceOfficer) Exam. 28.08.2011 (Paper-I)
21. On what sum does the differencebetween the compound interestand the simple interest for 3years at 10% is 31 ?(1) 1500 (2) 1200(3) 1100 (4) 1000(SSC CGL Prelim Exam. 27.02.200
(First Sitting)22. The difference between simple
and compound interests on asum of money at 4% per annumfor 2 years is 8. The sum is(1) 400 (2) 800(3) 4,000 (4) 5,000(SSC CGL Prelim Exam. 08.02.2004
(First Sitting)
3. The difference between thesimple and compound interest ona certain sum of money at 5%rate of interest per annum for 2years is 15. Then the sum is :(1) 6,500 (2) 5,500(3) 6,000 (4) 7,000(SSC CGL Prelim Exam. 24.02.2002
(Second Sitting)4. If the difference between the
compound interest and simpleinterest on a sum at 5% rate ofinterest per annum for threeyears is 36.60, then the sum is(1) 8000 (2) 8400(3) 4400 (4) 4800(SSC CGL Prelim Exam. 24.02.2002
(Middle Zone)5. The difference between com-
pound interest and simple inter-est on 2500 for 2 years at 4%per annum is(1) 40 (2) 45(3) 14 (4) 4
(SSC CPO S.I. Exam. 12.01.20036. The difference between simple and
compound interest (compoundedannually) on a sum of money for 2years at 10% per annum is 65.The sum is(1) 65650 (2) 65065(3) 6565 (4) 6500(SSC CGL Prelim Exam. 11.05.2003
(Second Sitting)7. The difference between the com-
pound interest (compounded an-nually) and the simple intereston a sum of 1000 at a certainrate of interest for 2 years is10. The rate of interest per an-num is :(1) 5% (2) 6%(3) 10% (4) 12%(SSC CGL Prelim Exam. 08.02.2004
(Second Sitting)8. If the difference between the
simple and compound interestson a sum of money for 2 years at4% per annum is 80, the sumis :(1) 5000 (2) 50000(3) 10000 (4) 1000
(SSC CPO S.I. Exam. 26.05.20059. The difference between simple
and compound interest on a cer-tain sum of money for 2 yearsat 4 per cent per annum is 1.The sum of money is :(1) 600 (2) 625(3) 560 (4) 650(SSC CGL Prelim Exam. 13.11.2005
(First Sitting) Exam. 26.05.2005)
10. The difference between thesimple and compound interest ona certain sum of money for 2years at 4% per annum is 4.The sum is(1) 2500 (2) 2,400(3) 2,600 (4) 2,000(SSC CGL Prelim Exam. 13.11.2005
(Second Sitting)11. If the difference between the
compound and simple interestson a certain sum of money for 3years at 5% per annum is15.25, then the sum is(1) 2,000 (2) 1,000(3) 1,500 (4) 2,500
(SSC CPO S.I. Exam. 03.09.2006)12. The difference between compound
interest and simple interest of asum for 2 years at 8 per cent is768. The sum is(1) 1,00,000 (2) 1,10,000
(3) 1,20,000 (4) 1,70,000(SSC Section Officer (Commercial
Audit) Exam. 26.11.2006(Second Sitting)
13. The difference between the com-pound and the simple interest ona sum for 2 years at 10% perannum, when the interest is com-pounded annually, is 28. If theinterest were compounded half-yearly, the difference in the twointerests will be(1) 44 (2) 28.35(3) 43.41 (4) 43.29
(SSC Section Officer (CommercialAudit) Exam. 30.09.2007
(Second Sitting)14. A sum of 6,000 is deposited
for 3 years at 5% per annumcompound interest (compoundedannually). The difference ofinterests for 3 and 2 years willbe(1) 75.00 (2) 30.75(3) 330.75 (4) 375.00
(SSC Section Officer (CommercialAudit) Exam. 30.09.2007
(Second Sitting)15. The difference between com-
pound interest (compounded an-nually) and simple interest on acertain sum of money at 10% perannum for 2 years is 40. Thesum is :
(1) 4000 (2) 3600(3) 4200 (4) 3200
(SSC CPO S.I. Exam. 16.12.2007)
SME–546
COMPOUND INTEREST
23. On a certain sum of money, thedifference between thecompound interest for a year,payable half-yearly, and thesimple interest for a year is
180. If the rate of interest inboth the cases is 10%, then thesum is(1) 60,000 (2) 72,000(3) 62,000 (4) 54,000(SSC Multi-Tasking (Non-Technical)
Staff Exam. 27.02.2011)
24. The difference between the com-pound interest and the simpleinterest on a certain sum at 5%per annum for 2 years is 1.50.The sum is
(1) 600 (2) 500(3) 400 (4) 300
(SSC Multi-Tasking Staff Exam.10.03.2013, Ist Sitting : Patna)
25. What sum will give 244 as thedifference between simple inter-est and compound interest at 10%
in 112
years compounded half
yearly ?(1) 40,000 (2) 36,000(3) 32,000 (4) 28,000
(SSC Graduate Level Tier-IIExam. 29.09.2013
26. The difference between simpleand compound interest com-pounded annually, on a certainsum of money for 2 years at 4%per annum is 1. The sum (in) is :
(1) 650 (2) 630(3) 625 (4) 640(SSC CGL Prelim Exam. 11.05.2003
(First Sitting)27. The difference between the com-
pound interest and simple inter-est for the amount 5,000 in 2years is 32. The rate of inter--est is(1) 5% (2) 8%(3) 10% (4) 12%(SSC CGL Tier-1 Exam. 19.06.2011
(Second Sitting)28. On what sum of money will the
difference between S.I and C.I
for 2 years at 5% per annum be
equal to 25 ?(1) 10,000 (2) 10,500(3) 9,500 (4) 9000
(SSC CGL Tier-IRe-Exam. (2013) 27.04.2014)
29. The difference between the com-pound interest and simple inter-est on a certain sum for 2 years
at 10% per annum is 300.Find the sum.
(1) 31,000 (2) 31,500
(3) 30,000 (4) 30,500(SSC CGL Tier-I
Re-Exam. (2013) 27.04.2014)
30. Find the difference between thecompound interest and thesimple interest on 32,000 at10% p.a. for 4 years.
(1) 2051.20 (2) 2052.50
(3) 2025.20 (4) 2501.20(SSC CHSL DEO & LDC
Exam. 16.11.2014)
31. On what sum of money will thedifference between simple inter-est and compound interest for 2years at 5% per annum be equalto Rs. 63?
(1) Rs. 24,600 (2) Rs. 24,800
(3) Rs. 25,200 (4) Rs. 25,500(SSC CHSL (10+2) LDC, DEO & PA/SA
Exam, 01.11.2015, IInd Sitting)
32. The difference between simpleand compound interests com-pounded annually on a certainsum of money for 2 years at 4%per annum is Re. 1. The sum (inRs.) is :
(1) 620 (2) 630
(3) 640 (4) 625(SSC CGL Tier-I (CBE)
Exam. 09.09.2016) (Ist Sitting)
33. The difference between C I andS I for 2 years at 10% rate ofinterest is Rs. 4. Find the sum ofmoney.
(1) Rs. 400 (2) Rs. 200
(3) Rs. 300 (4) Rs. 800(SSC CPO SI & ASI, Online
Exam. 06.06.2016) (IInd Sitting)
34. The difference between simpleand compound interest (com-pounded annually) on a sum ofmoney for 3 years at 10% perannum is Rs. 93. The sum (in Rs.)is :
(1) 30000 (2) 30300
(3) 3000 (4) 3030(SSC CGL Tier-I (CBE)
Exam. 27.08.2016) (Ist Sitting)
35. The difference between com-pound interest and simple inter-est on a certain sum of moneyfor 2 years at 5% per annum isRs. 41. What is the sum of mon-ey ?
(1) Rs. 7200 (2) Rs. 9600(3) Rs. 16400 (4) Rs. 8400
(SSC CGL Tier-I (CBE)Exam. 28.08.2016) (IInd Sitting)
36. If the difference of the compoundinterest and the simple intereston a sum of money for 3 years isRs. 186. Find the sum of money,if the rate of interest in both cas-es be 10%.
(1) Rs. 5500 (2) Rs. 7200(3) Rs. 6500 (4) Rs. 6000
(SSC CGL Tier-II (CBE)Exam. 30.11.2016)
37. The difference between the sim-ple interest and compound inter-est (compounded annually) on Rs.40,000 for 3 years at 8% perannum is :
(1) Rs. 684.32 (2) Rs. 788.48
(3) Rs. 784.58 (4) Rs. 4000(SSC CGL Tier-I (CBE)
Exam. 28.08.2016 (IST Sitting)
38. The difference between compoundinterest and simple interest on anamount of Rs. 15,000 for 2 yearsis Rs. 96. The rate of interest perannum is
(1) 6% (2) 7%
(3) 8% (4) 9%(SSC CGL Tier-I (CBE)
Exam. 01.09.2016 (IIIrd Sitting)
39. The difference between com-pound interest and simple inter-est on Rs. 5000 for 2 years at8% per annum payable yearly is
(1) Rs. 30 (2) Rs. 31(3) Rs. 33 (4) Rs. 32
(SSC CGL Tier-I (CBE)Exam. 03.09.2016 (IIIrd Sitting)
40. If the difference between thecompound interest and the sim-ple interest on a certain sum atthe rate of 5% per annum for 2years is Rs. 20, then the sum is :
(1) Rs. 2000 (2) Rs. 4000
(3) Rs. 6000 (4) Rs. 8000(SSC CGL Tier-I (CBE)
Exam. 07.09.2016 (IInd Sitting)
SME–547
COMPOUND INTEREST
(1) 9 years (2) 27 years
(3) 6 years (4) 3 years(SSC Graduate Level Tier-II
Exam.16.09.2012) 14. A sum of money becomes 1.331
times in 3 years as compoundinterest. The rate of interest is(1) 8% (2) 7.5%(3) 10% (4) 50%
(SSC Multi-Tasking StaffExam. 17.03.2013, IInd Sitting)
15. If a sum of money compoundedannually becomes 1.44 times ofitself in 2 years, then the rate ofinterest per annum is(1) 25% (2) 22%(3) 21% (4) 20%
(SSC Graduate Level Tier-IIExam. 29.09.2013
16. If the amount is 338
times the
sum after 3 years at compoundinterest compounded annually,then the rate of interest per an-num is(1) 25% (2) 50%
(3) 1623
% (4) 3313
%
(SSC CHSL DEO & LDC Exam.10.11.2013, Ist Sitting)
TYPE–V
1. A sum of money amounts to4,840 in 2 years and to 5,324in 3 years at compound interestcompounded annually. The rateof interest per annum is :
(1) 10% (2) 9%(3) 11% (4) 8%
(SSC CPO S.I. Exam. 16.12.2007)2. A certain sum of money amounts
to 2,420 in 2 years and 2,662in 3 years at some rate of com-pound interest, compounded an-nually. The rate of interest perannum is(1) 6% (2) 8%(3) 9% (4) 10%
(SSC CPO S.I. Exam. 09.11.2008) 3. An amount of money at com-
pound interest grows up to 3,840 in 4 years and up to 3,936 in 5 years. Find the rate
of interest.(1) 2.5% (2) 2%(3) 3.5% (4) 2.05%
(SSC Graduate Level Tier-IIExam.16.09.2012)
TYPE–IV
1. If the amount is 2.25 times ofthe sum after 2 years at com-pound interest (compound annu-ally), the rate of interest per an-num is :(1) 25% (2) 30%(3) 45% (4) 50%(SSC CGL Prelim Exam. 04.07.1999
(Second Sitting)
2. A sum of money doubles itself in4 years at compound interest. Itwill amount to 8 times itself at thesame rate of interest in :(1) 18 years (2) 12 years(3) 16 years (4) 24 years(SSC CGL Prelim Exam. 24.02.2002
(First Sitting) & (SSC CPO S.I.Exam. 16.12.2007)
3. A sum borrowed under com-pound interest doubles itself in10 years. When will it becomefourfold of itself at the same rateof interest ?(1) 15 years (2) 20 years(3) 24 years (4) 40 years(SSC CGL Prelim Exam. 24.02.2002
(Second Sitting)
4. A sum of money becomes eighttimes of itself in 3 years at com-pound interest. The rate of inter-est per annum is(1) 100% (2) 80%(3) 20% (4) 10%(SSC CGL Prelim Exam. 08.02.2004
(First Sitting)
5. A sum of money invested at com-pound interest doubles itself in6 years. At the same rate of in-terest it will amount to eighttimes of itself in :(1) 15 years (2) 12 years(3) 18 years (4) 10 years(SSC CGL Prelim Exam. 24.02.2002
(Middle Zone) & (SSC CGL PrelimExam. 13.11.2005 (First Sitting)
6. A sum of money placed at com-pound interest doubles itself in5 years. In how many years, itwould amount to eight times ofitself at the same rate of interest ?(1) 10 years (2) 15 years(3) 7 years (4) 20 years(SSC CGL Prelim Exam. 13.11.2005
(IInd Sitting) & (SSC CPO S.I. Exam.06.09.2009) & (SSC CAPs S.I. &
CISF ASI Exam. 23.06.2013)
7. A sum of money at compoundinterest doubles itself in 15 years.It will become eight times of it-self in(1) 45 years (2) 48 years(3) 54 years (4) 60 years
(SSC CGL Prelim Exam. 04.07.1999 (IstSitting) & (SSC CGL Tier-I
Exam. 16.05.2010 (First Sitting)
8. A sum of 12,000, deposited atcompound interest becomesdouble after 5 years. How muchwill it be after 20 years ?(1) 1,44,000 (2) 1,20,000(3) 1,50,000 (4) 1,92,000(SSC CGL Tier-I Exam. 16.05.2010
(IInd Sitting) & (SSC CGL Tier-I19.06.2011 (IInd Sitting)
9. At what rate percent per annumof compound interest, will a sumof money become four times ofitself in two years ?(1) 100% (2) 75%(3) 50% (4) 20%
(SSC (South Zone) InvestigatorExam. 12.09.2010)
10. A sum of money becomes dou-ble in 3 years at compound in-terest compounded annually. Atthe same rate, in how manyyears will it become four timesof itself ?(1) 4 years (2) 6 years(3) 6.4 years (4) 7.5 years
(SSC CPO S.I.Exam. 12.12.2010 (Paper-I)
11. A sum of money becomes eighttimes in 3 years, if the rate iscompounded annually. In howmuch time will the same amountat the same compound ratebecome sixteen times?(1) 6 years (2) 4 years(3) 8 years (4) 5 years(SSC CGL Tier-1 Exam. 19.06.2011
(First Sitting)
12. A sum of money placed at com-pound interest doubles itself in4 years. In how many years willit amount to four times itself ?
(1) 12 years (2) 13 years
(3) 8 years (4) 16 years(SSC CGL Tier-1 Exam.
26.06.2011 (First Sitting)13. A sum of money at compound in-
terest amounts to thrice itself in3 years. In how many years willit be 9 times itself ?
SME–548
COMPOUND INTEREST
4. A certain amount of money at r%,compounded annually after twoand three years becomes 1440and 1728 respectively. r is(1) 5 (2) 10(3) 15 (4) 20
(SSC CHSL DEO & LDC Exam.28.10.2012 (Ist Sitting)
5. The compound interest on a cer-tain sum for two successive yearsare 225 and 238.50. The rateof interest per annum is :
(1) 712
% (2) 5%
(3) 10% (4) 6%(SSC CHSL DEO & LDC Exam.
21.10.2012 (IInd Sitting)6. An amount of money appreciates
to 7,000 after 4 years and to10,000 after 8 years at a certaincompound interest compoundedannually. The initial amount ofmoney was(1) 4,700 (2) 4,900(3) 4,100 (4) 4,300
(SSC Multi-Tasking StaffExam. 17.03.2013, Ist Sitting)
7. A sum of money invested atcompound interest amounts to 650 at the end of first year and 676 at the end of second year..
The sum of money is :(1) 600 (2) 540(3) 625 (4) 560(SSC CGL Prelim Exam. 24.02.2002
(Ist Sitting) & (SSC CPO S.I.Exam. 07.09.2003)
8. A sum of money invested at com-pound interest amounts in 3years to 2,400 and in 4 yearsto 2,520. The interest rate perannum is :(1) 5% (2) 6%(3) 10% (4) 12%(SSC CGL Prelim Exam. 24.02.2002
(Second Sitting)9. A sum becomes 4500 after two
years and 6750 after four yearsat compound interest. The sum is(1) 4000 (2) 2500(3) 3000 (4) 3050(SSC CGL Prelim Exam. 24.02.2002
(Middle Zone) & (SSC CGLExam. 13.11.2005)
10. A sum of money at compoundinterest will amount to 650 atthe end of the first year and676 at the end of the secondyear. The amount of money is(1) 1,300 (2) 650(3) 1,250 (4) 625
(SSC CGL Tier-I Re-Exam. (2013)20.07.2014 (Ist Sitting)
11. On a certain sum of money, thesimple interest for 2 years is Rs.350 at the rate of 4% per annum.It was invested at compound in-terest at the same rate for the sameduration as before, how much moreinterest would be earned?(1) Rs. 3.50 (2) Rs. 7(3) Rs. 14 (4) Rs. 35
(SSC CAPFs (CPO) SI & ASI,Delhi Police Exam. 05.06.2016)
(Ist Sitting)12. A certain amount grows at an an-
nual interest rate of 12%, com-pounded monthly. Which of thefollowing equations can be solvedto find the number of years, y,that it would take for the invest-ment to increase by a factor of64 ?(1) 64 = (1.01)12y
(2)1
64104 12= ( . ) y
(3) 64 = (1.04)12y
(4) 8 = (1.01)6y(SSC CPO SI & ASI, Online
Exam. 06.06.2016) (IInd Sitting)13. The compound interest on a cer-
tain sum for 2 years at 10% perannum is Rs. 525 . The simpleinterest on the same sum for dou-ble the time at half the rate percent per annum is :(1) Rs. 520 (2) Rs. 550(3) Rs. 500 (4) Rs. 515
(SSC CGL Tier-I (CBE)Exam. 30.08.2016) (IInd Sitting)
14. A sum of money is invested at20% compound interest (com-pounded annually). It would fetchRs. 723 more in 2 years if inter-est is compounded half yearly.The sum is(1) Rs.15,000 (2) Rs.30,000(3) Rs.20,000 (4) Rs.7,500
(SSC CGL Tier-II (CBE)Exam. 30.11.2016)
TYPE–VI
1. A builder borrows 2550 to bepaid back with compound inter-est at the rate of 4% per annumby the end of 2 years in two equalyearly instalments. How much willeach instalment be ?(1) 1352 (2) 1377(3) 1275 (4) 1283(SSC CGL Prelim Exam. 27.02.2000
(First Sitting)2. A man buys a scooter on making
a cash down payment of 16224and promises to pay two moreyearly instalments of equivalent
amount in next two years. If therate of interest is 4% per annum,compounded yearly, the cashvalue of the scooter, is(1) 40000 (2) 46824(3) 46000 (4) 50000(SSC CGL Prelim Exam. 04.02.2007
(Second Sitting)3. Kamal took 6800 as a loan
which along with interest is to berepaid in two equal annual instal-ments. If the rate of interest is
1212
%, compounded annually,
then the value of each instalmentis(1) 8100 (2) 4150(3) 4050 (4) 4000(SSC CGL Prelim Exam. 27.07.2008
(First Sitting)4. A loan of 12,300 at 5% per an-
num compound interest, is to berepaid in two equal annualinstalments at the end of everyyear. Find the amount of eachinstalment.(1) 6,651 (2) 6,615(3) 6,516 (4) 6,156
(SSC CPO S.I. Exam. 06.09.2009)5. A sum of 210 was taken as a
loan. This is to be paid back intwo equal instalments. If the rateof interest be 10% compoundedannually, then the value of eachinstalment is(1) 127 (2) 121(3) 210 (4) 225
(SSC CHSL DEO & LDCExam. 9.11.2014)
6. Rs. 16,820 is divided betweentwo brothers of age 27 years and25 years. They invested theirmoney at 5% per annum com-pound interest in such a way thatboth will receive equal money atthe age of 40 years. The share(in Rs.) of elder brother is
(1) 8,280 (2) 8,410
(3) 8,820 (4) 8,000(SSC CGL Tier-II Exam,
2014 12.04.2015 (Kolkata Region)TF No. 789 TH 7)
7. A sum of money is paid back intwo annual instalments of Rs. 17,640 each, allowing 5% compoundinterest compounded annually.The sum borrowed was(1) Rs. 32,800 (2) Rs. 32,200
(3) Rs. 32,000 (4) Rs. 32,400(SSC CGL Tier-II Exam,
25.10.2015, TF No. 1099685)
SME–549
COMPOUND INTEREST
8. Mr. Dutta desired to deposit hisretirement benefit of Rs. 3 lacspartly to a post office and partlyto a bank at 10% and 6% inter-ests respectively. If his monthlyinterest income was Rs. 2000,then the difference of his depos-its in the post office and in thebank was :(1) Rs. 50,000 (2) Rs. 40,000(3) Nil (4) Rs.1,00,000
(SSC CHSL (10+2) LDC, DEO& PA/SA Exam, 06.12.2015(Ist Sitting) TF No. 1375232)
9. The income of a company in-creases 20% per year. If the in-come is Rs. 26,64,000 in the year2012, then its income in the year2010 was :(1) Rs. 28,55,000(2) Rs. 18,50,000(3) Rs. 28,20,000(4) Rs. 21,20,000
(SSC CHSL (10+2) LDC, DEO& PA/SA Exam, 06.12.2015
(IInd Sitting) TF No. 3441135)
TYPE–VII
1. A person deposited a sum of6,000 in a bank at 5% per an-num simple interest. Anotherperson deposited 5,000 at 8%per annum compound interest.After two years, the difference oftheir interests will be(1) 230 (2) 232(3) 832 (4) 600
(SSC CPO S.I. Exam. 03.09.2006)2. A money-lender borrows money
at 4% per annum and pays theinterest at the end of the year.He lends it at 6% per annum com-pound interest compounded halfyearly and receives the interestat the end of the year. In this way,he gains 104.50 a year. Theamount of money he borrows, is(1) 6,000 (2) 5,500(3) 5,000 (4) 4,500(SSC CGL Prelim Exam. 04.02.2007
(First Sitting)3. A sum of 13,360 was borrowed
at 8 34 % per annum compound
interest and paid back in twoyears in two equal annual instal-ments. What was the amount ofeach instalment ?(1) 5,769 (2) 7,569(3) 7,009 (4) 7,500
(SSC CGL Prelim Exam. 27.07.2008(Second Sitting)
4. Sita deposited 5,000 at 10%simple interest for 2 years. Howmuch more money will Sita havein her account at the end of twoyears, if it is compounded semi-annually.(1) 50 (2) 40
(3) 77.50 (4) 85.50(SSC Graduate Level Tier-II
Exam.16.09.2012)5. What does 250 amounts to in
2 years with compound interestat the rate of 4% in the 1st yearand 8% in the second year ?(1) 280 (2) 280.80(3) 468 (4) 290.80
(SSC Constable (GD)Exam. 12.05.2013 Ist Sitting)
6. A man gave 50% of his savingsof 84,100 to his wife and di-vided the remaining sum amonghis two sons A and B of 15 and13 years of age respectively. Hedivided it in such a way that eachof his sons, when they attain theage of 18 years, would receivethe same amount at 5% com-pound interest per annum. Theshare of B was(1) 20,000 (2) 20,050(3) 22,000 (4) 22,050(SSC CGL Tier-I Exam. 19.10.2014)
7. Find the rate percent per annum,if Rs. 2000 amounts to Rs.2,315.25 in a year and a half,interest being compounded halfyearly.(1) 11.5% (2) 10%(3) 5% (4) 20%
(SSC CAPFs SI, CISF ASI & DelhiPolice SI Exam, 21.06.2015
IInd Sitting)8. A sum of money placed at com-
pound interest doubles itself in5 years. It will amount to eighttimes of itself at the same rateof interest in(1) 20 years (2) 10 years
(3) 12 years (4) 15 years(SSC CGL Tier-II Exam,
25.10.2015, TF No. 1099685)
9. The sum of money which whengiven on compound interest at18% per annum would fetch Rs.960 more when the interest ispayable half yearly than when itwas payable annually for 2 yearsis :(1) Rs.60,000 (2) Rs. 30,000(3) Rs. 40,000 (4) Rs. 50,000
(SSC CHSL (10+2) LDC, DEO& PA/SA Exam, 15.11.2015(Ist Sitting) TF No. 6636838)
10. The amount on Rs. 25,000 in 2years at annual compound inter-est, if the rates for the succes-sive years be 4% and 5% perannum respectively is :(1) Rs. 30,000 (2) Rs. 26,800(3) Rs. 27,300 (4) Rs. 28,500
(SSC CHSL (10+2) LDC, DEO& PA/SA Exam, 15.11.2015(Ist Sitting) TF No. 6636838)
11. The amount of Rs. 10,000 after2 years, compounded annuallywith the rate of interest being 10%per annum during the first yearand 12% per annum during thesecond year, would be (in rupees)(1) 11,320 (2) 12,000(3) 12,320 (4) 12,500
(SSC CGL Tier-I (CBE)Exam. 02.09.2016) (Ist Sitting)
12. On a certain principal if the sim-ple interest for two years is Rs.1400 and compound interest forthe two years is Rs. 1449, whatis the rate of interest?(1) 7 per cent (2) 3.5 per cent(3) 14 per cent (4) 10.5 per cent
(SSC CHSL (10+2) Tier-I (CBE)Exam. 15.01.2017) (IInd Sitting)
13. A man borrowed some money andagreed to pay-off by paying Rs.3150 at the end of the 1st yearand Rs. 4410 at the end of the2nd year. If the rate of compoundinterest is 5% per annum, thenthe sum is(1) Rs. 5000 (2) Rs. 6500(3) Rs. 7000 (4) Rs. 9200
(SSC CGL Tier-II (CBE)Exam. 12.01.2017)
14. Rs. 260200 is divided betweenRam and Shyam so that theamount that Ram receives in 4years is the same as that Shyamreceives in 6 years. If the inter-est is compounded annually at therate of 4% per annum then Ram’sshare is(1) Rs. 125000 (2) Rs. 135200(3) Rs. 152000 (4) Rs. 108200
(SSC CGL Tier-II (CBE)Exam. 12.01.2017)
15. B borrows 5,000 from A at 6%p.a. simple interest and lends itto C at compound interest of10% p.a. If B collects the moneyback from C after 2 years andrepays A, the profit made by Bin the transaction is(1) 1,050 (2) 500(3) 450 (4) 600
(SSC Multi-Tasking StaffExam. 30.04.2017)
SME–550
COMPOUND INTEREST
SHORT ANSWERS
TYPE-I
1. (2) 2. (2) 3. (3) 4. (1)
5. (3) 6. (2) 7. (3) 8. (4)
9. (3) 10. (3) 11. (1) 12. (1)
13. (3) 14. (1) 15. (4) 16. (3)
17. (1) 18. (3) 19. (2) 20. (1)
21. (1) 22. (4) 23. (1) 24. (3)
25. (4) 26. (2) 27. (3) 28. (2)
29. (1) 30. (2) 31. (2) 32. (2)
33. (1) 34. (3) 35. (2) 36. (2)
37. (4) 38. (3) 39. (1) 40. (3)
41. (3) 42. (4) 43. (4) 44. (4)
45. (3) 46. (2) 47. (2) 48. (3)
49. (3) 50. (4) 51. (2) 52. (3)
53. (3) 54. (3) 55. (1) 56. (2)
57. (1) 58. (3) 59. (1) 60. (1)
61. (2) 62. (2) 63. (1) 64. (1)
65. (1) 66. (2)
TYPE-II
1. (3) 2. (2) 3. (3) 4. (2)
5. (3) 6. (1) 7. (2) 8. (3)
9. (4) 10. (4) 11. (4) 12. (4)
13. (4) 14. (4) 15. (1) 16. (2)
17. (1) 18. (1) 19. (4) 20. (2)
21. (3) 22. (2) 23. (3) 24. (2)
25. (4) 26. (2) 27. (4)
TYPE-III
1. (1) 2. (2) 3. (3) 4. (4)
5. (4) 6. (4) 7. (3) 8. (2)
9. (2) 10. (1) 11. (1) 12. (3)
13. (3) 14. (3) 15. (1) 16. (1)
17. (2) 18. (1) 19. (2) 20. (3)
21. (4) 22. (4) 23. (2) 24. (1)
25. (3) 26. (3) 27. (2) 28. (1)
29. (3) 30. (1) 31. (3) 32. (4)
33. (1) 34. (1) 35. (3) 36. (4)
37. (2) 38. (3) 39. (4) 40. (4)
TYPE-IV
1. (4) 2. (2) 3. (2) 4. (1)
5. (3) 6. (2) 7. (1) 8. (4)
9. (1) 10. (2) 11. (2) 12. (3)
13. (3) 14. (3) 15. (4) 16. (2)
TYPE-V
1. (1) 2. (4) 3. (1) 4. (4)
5. (4) 6. (2) 7. (3) 8. (1)
9. (3) 10. (4) 11. (2) 12. (1)
13. (3) 14. (2)
TYPE-VI
1. (1) 2. (2) 3. (3) 4. (2)
5. (2) 6. (3) 7. (1) 8. (3)
9. (2)
TYPE-VII
1. (2) 2. (3) 3. (2) 4. (3)
5. (2) 6. (1) 7. (2) 8. (4)
9. (4) 10. (3) 11. (3) 12. (1)
13. (3) 14. (2) 15. (3)
EXPLANATIONS
TYPE-I
1. (2) Using Rule 1,P = 3000, A = 3993, n = 3years
A P r n= +F
HGIKJ1
100
\ +FHG
IKJ =1
100r
P
n A
1100
39933000
3+F
HIK =
r =
13311000
1100
1110
3 3+F
HIK = F
HIK
r
Þ 1100
1110
+ =r
Þr
1001110
1= –
Þr
1001
10= Þ r =
10010
\ r = 10%2. (2) Using Rule 1,
A = +FHG
IKJ10 000 1 2
100
4,
= FHG
IKJ10 000 51
50
4, =10824.3216
\ Interest= 10,824.3216 – 10,000= 824.32
3. (3) Using Rule 1,According to question,
2420 2000 1 10100
= +FHG
IKJ
t
24202000
1110
= FHG
IKJ
t
ort
, 1110
121100
FHG
IKJ =
or,1110
1110
2FHG
IKJ = F
HGIKJ
t
\ t = 2 years4. (1) Using Rule 1,
Let the required time be n years.Then,
1331 = 1000 110100
+FHG
IKJn
\ = FHG
IKJ
LNMM
OQPPP P 1+
1001r
n
Þ =+F
HGIKJ
13311000
10 110
n
Þ FHG
IKJ = F
HGIKJ
1110
1110
3n
Þ n = 35. (3) Using Rule 1,
Let the principal be P..
\ 270.40 = P 14
100
2+F
HGIKJ
Þ 270.40 = P (1 + 0.04)2
Þ P =270 40
104 104.
. .´= 250
SME–551
COMPOUND INTEREST
6. (2) Using Rule 1,Let the sum be P and rate ofinterest be R% per annum. Then,
PR
1100
96802
+FHG
IKJ = ...(i)
PR
1100
106483
+FHG
IKJ = ...(ii)
On dividing equation (ii) by (i)
1100
106489680
+ =R
ÞR
100106489680
1= -
=10648 9680
9680-
ÞR
1009689680
= =1
10
Þ R =1
10100 10´ = %
7. (3) Using Rule 1,Let the rate per cent per annumbe r. Then,
2500 = 2304 1100
2
+FHG
IKJ
r
Þ 1100
25002304
5048
2 2
+FHG
IKJ = = F
HGIKJ
r
Þ 1100
5048
2524
+ = =r
Þr
1002524
1124
= - =
Þ r =10024
256
416
= = %
8. (4) Using Rule 1,Let the sum be x.
\ 1352 = x 14
100
2
+FHG
IKJ
Þ 1352 = x 1125
2
+FHG
IKJ
Þ 1352 = x2625
2FHG
IKJ
Þ x =1352 25 25
26 26´ ´
´
= 1250
9. (3) Using Rule 1,The interest is compounded quar-terly.
\R =204
5%=
Time = 3 quarters
\ C.I. = P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
= +FHG
IKJ -
LNMM
OQPP16000 1
5100
13
= FHG
IKJ -
LNMM
OQPP16000
2120
13
=-F
HGIKJ16000
9261 80008000
= ´1600012618000
= 2522
10. (3) Using Rule 3,Amount
= +FHG
IKJ +FHG
IKJ +FHG
IKJP 1
R100
1R100
1R100
1 2 3
= +FHG
IKJ +FHG
IKJ +FHG
IKJ10000 1
4100
15
1001
6100
= ´ ´ ´100002625
2120
5350
A = 11575.2\ C.I. = (11575.2–10000)= 1575.2
11. (1) Using Rule 3,Amount
= +FHG
IKJ +FHG
IKJ2000 1 4
1001 3
100= 2000 ×1.04 ×1.03= 2142.40\ CI = (2142.40 – 2000)= 142.40
12. (1) Using Rule 1,Let the rate of CI be R per centper annum.
\ CI = +FHG
IKJ -
LNMM
OQPPP 1 R
1001
T
Þ 5044 = 32000 1R
4001
3
+FHG
IKJ -
LNMM
OQPP
[Q Interest is compounded quar--terly]
Þ = +FHG
IKJ -
504432000
1 R400
13
Þ +FHG
IKJ -1 R
4001 = 1261
8000
3
Þ +FHG
IKJ =1 R
4001 + 1261
8000
3
Þ +FHG
IKJ = = F
HGIKJ1 R
40092618000
3 2120
3
Þ + = Þ = - =1 R400
R400
2120
2120
1 120
Þ = =R 40020
20
13. (3) Using Rule 1,
Amount = P 1R
100
t+
FHG
IKJ
= 8000 115100
+FHG
IKJ2
13
= 8000 1320
+FHG
IKJ +
´FHG
IKJ
2
13
20 3
= 8000 ×2320
2320
2120
´ ´
= 11109\ Compound Interest= (11109 – 8000) = 3109.
14. (1) Using Rule 1 and 2,The rate of interest is compound-ed half yearly,\ r = 10% per half year
Let time =T2 years = half years
According to the question,
Amount = P 1R
100
t+
FHG
IKJ
Þ 13310 = 10000 110100
+FHG
IKJ
T
Þ1331010000
1110
=FHG
IKJ
T
Þ1110
13311000
1110
3FHG
IKJ = =
FHG
IKJ
T
Þ T = 3 half years =1 12 years
SME–552
COMPOUND INTEREST
15. (4) Let the principal be x. Now,
C.I. = P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
Þ 1261 = x 15
1001
3
+FHG
IKJ -
LNMM
OQPP
Þ 1261 = x92618000
1-FHG
IKJ
Þ 1261 = x9261 8000
8000-F
HGIKJ
=12618000
x
Þ x =1261 8000
1261´
= 8000
16. (3) Using Rule 1,Let the sum be P.As, the interest is compoundedhalf-yearly,\ R = 2%, T = 2 half years
\ A = P 1R
100
T+
FHG
IKJ
Þ 7803 = P 12
100
2+
FHG
IKJ
Þ 7803 = P 1150
2+
FHG
IKJ
Þ 7803 = P5150
´ ´5150
Þ P =´ ´
´7803 50 50
51 51= 7500
17. (1) Using Rule 1,
5832 = P 18
100
2+
FHG
IKJ
Þ 5832 = P 1225
2+
FHG
IKJ
Þ 5832 = P2725
´ ´2725
Þ P =5832 25 25
27 27´ ´
´= 5000
18. (3) Amount
= 6000 110100
1
12
10
100+F
HGIKJ ´ +
´F
HGGG
I
KJJJ
= 60001110
2120
´ ´ = 6930
Aliter : Using Rule 4,
Here, t = nF
A = P 1100
1100
+FHG
IKJ +
FHG
IKJ
r rFn
\ CI = (6930 – 6000) = 93019. (2) Using Rule 1 and 2,
Interest is compounded half year-ly.\ Rate of interest = 5%
Time =n
2 years (let)
or n half-years
A = P 1R
100
T+
FHG
IKJ
Þ 9261 = 8000 15
100+
FHG
IKJn
Þ 92618000
2120
=FHG
IKJn
Þ2120
2120
3FHG
IKJ =
FHG
IKJn
Þ n = 3 half years
=32
years = 112
years
20. (1) Using Rule 1,
A = P 1100
+FHG
IKJ
R T
Let rate be 'r '
Þ1102 50
10001
100
2.= +FHG
IKJ
r
Þ 1102510000
1100
2= +FHG
IKJ
r
Þ 105100
1100
2 2FHG
IKJ = +
FHG
IKJ
r
Þ 1 +r
100 =
105100
Þ r
1005
100=
Þ r = 5%21. (1) Using Rule 1 and 2,
Rate = 10% per annum = 5% halfyearly
A = P 1R
100
T+
FHG
IKJ
Þ 926.10 = 800 15
100
T+
FHG
IKJ
Þ92618000
=2120
TFHG
IKJ
Þ2120
2120
3 TFHG
IKJ =
FHG
IKJ
\ Time = 3 half years
= 112
years
22. (4) Using Rule 1,
A = P 1R
100
T+
FHG
IKJ
= 6000 15
100
2+
FHG
IKJ
= 6000 ×2120
2120
´ = 6615
23. (1) Using Rule 1 and 2,Let the required time be t years.Interest is compounded halfyearly.\ Time = 2t half years
and rate =202
= 10%
\ 1000 110100
2+F
HGIKJ
t
= 1331
Þ1110
2FHG
IKJ
t=
13311000
Þ1110
2FHG
IKJ
t= FHG
IKJ
1110
3Þ 2t = 3
\ t =32
years or 112
years
24. (3) Using Rule 1,
A = P 1R
100
T
+FHG
IKJ
Þ 30000 + 4347
= 30000 17
100
T
+FHG
IKJ
Þ3434730000
107100
= FHG
IKJ
T
Þ1144910000
107100
107100
2
= FHG
IKJ = F
HGIKJ
T
Þ Time = 2 years
SME–553
COMPOUND INTEREST
25. (4) Using Rule 1,If the rate of C.I. be r% per an-num, then
A = P 1100
+FHG
IKJ
RT
Þ 8820 = 8000 1100
2
+FHG
IKJ
r
Þ88208000
1100
2
= +FHG
IKJ
r
Þ441400
2120
1100
2 2
= FHG
IKJ = +F
HGIKJ
r
Þ 1 +r
100 =
2120
Þr
100 =
2120
– 1 =120
Þ r =120
× 100
\ r = 5% per annum26. (2) Using Rule 3,
A = Pr r
1100
1100
1 2+FHG
IKJ +FHG
IKJ
= 10000 110
1001
12100
+FHG
IKJ +FHG
IKJ
= 100001110
2825
´ ´
= 1232027. (3) Using Rule 1,
CI = P 1R
100–1
T
+FHG
IKJ
LNMM
OQPP –
PR100
Þ 420 = P 15
1001
2
+FHG
IKJ -
LNMM
OQPP -
´P 5100
Þ 420 = P2120
12F
HGIKJ -
LNMM
OQPP -
5P100
Þ 420 =41P400
5P100
- =21400
P
Þ P =420 400
21´
= 8000
28. (2) Using Rule 1,Amount
= 2000 15
1002000 1
5100
2
+FHG
IKJ + +F
HGIKJ
= 20002120
20002120
2
´ FHG
IKJ + F
HGIKJ
= 20002120
4120
´ ´ = 4305
\ Required amount
= 4305 + 2000 = 630529. (1) Using Rule 1 and 2,
Time = t half year and R = 5% per half year
\ A = P 1R
100
T
+FHG
IKJ
Þ9261080000
15
100= +FHG
IKJ
T
Þ92618000
2120
= FHG
IKJ
T
Þ T = 3 half years or 112
years
Þ2120
2120
3FHG
IKJ = F
HGIKJ
T
30. (2) If each instalment be x, then
Present worth of first instalment
=
x x
110100
1011+
=
Present worth of second instal-ment
=x
x
110100
1001212
+FHG
IKJ
=
\1011
100121
21000x x+ =
Þ 110 100
12121000
x x+=
Þ 210x = 21000 × 121
Þ x =21000 121
210´
x = 12100
Aliter : Using Rule 9,Here, n = 2, p = 21000,r = 10%Each annual instalment
=
P
r r100
100100
100
2
+FHG
IKJ +
+FHG
IKJ
=
21000
100110
100110
2
+ FHG
IKJ
=
21000100110
1000012100
+
=
210001011
100121
+
=21000
110 100121
+´
=21000210
121´
= 1210031. (2) Using Rule 1,
A = P 1R
100
T+F
HGIKJ
Þ 882 = 800 15
100
T+F
HGIKJ
Þ 882800
=2120
TFHG
IKJ
Þ 441400
=2120
2FHG
IKJ =
2120
TFHG
IKJ
\ T = 2 years32. (2) Using Rule 1,
C.I. = P 1 1+FHG
IKJ -
LNMM
OQPP
R100
T
= 5000 1 1+FHG
IKJ -
LNMM
OQPP
10100
3
= 50001110
13F
HGIKJ -
LNMM
OQPP
C.I.=5000 331
1000´
= 1655
33. (1) Using Rule 1 and 2,
A = P 1R
100
T
+FHG
IKJ
Þ33623200
110400
4
= +FHG
IKJ
t
Þ16811600
4140
4
= FHG
IKJ
t
SME–554
COMPOUND INTEREST
Þ4140
4140
2 4FHG
IKJ = F
HGIKJ
t
Þ 4t = 2 Þ t =12
year
34. (3) Using Rule 1,
Let the principal be Rs. P
\ C.I. = P 1R
1001
2
+FHG
IKJ -
LNMM
OQPP
Þ 328 = P 15
1001
2
+FHG
IKJ -
LNMM
OQPP
Þ 328 = P2120
12F
HGIKJ -
LNMM
OQPP
Þ 328 = P441400
1-FHG
IKJ
Þ 328 = P441 – 400
400FHG
IKJ
Þ 328 =41P400
Þ P =328 400
41´
= 3200
35. (2) Present worth of bike
= P 1R
100
T
-FHG
IKJ
= 62500 14
100
2-
FHG
IKJ
= 62500 1125
2-
FHG
IKJ
= 6250025 1
25
2-FHG
IKJ
=62500 24 24
25 25´ ´´
= 5760036. (2) C.I. – S.I.
= 615 – 600 = 15
S.I. for 1 year =6002
= 300
\ S.I. for 1 year on 300
= 15
\ Rate =15 100300 1
´´ = 5%
\P R T100
= 600
Þ P ´´5 2
100 = 600
Þ P = 600 × 10 = 600037. (4) Using Rule 1,
A = P 1100
+FHG
IKJ
RT
Þ 13230 = 12000 15
100+F
HGIKJn
Þ 1323012000
1120
= +FHG
IKJ
n
Þ 441400
2120
= FHG
IKJn
Þ 2120
2120
2FHG
IKJ = F
HGIKJ
n
Þ n = 2 years38. (3) Using Rule 1,
Principal (P) = Rs. SRate (R) = 2r% per annum
\ Amount = P 1R
100
T+
FHG
IKJ
= S 12r
100
3+
FHG
IKJ = S 1
r50
3+
FHG
IKJ
39. (1) Using Rule 1,
A = P 1100
R T+
FHG
IKJ
Þ2420 = P 110100
2
+FHG
IKJ
Þ2420 = P 11
10
2
+FHG
IKJ = P
1110
2FHG
IKJ
ÞP =2420 10 10
11 11´ ´´ = Rs. 2000
40. (3) Using Rule 1,Let principal be Rs. P.
Interest in 1 year =PRT100
=P 10100´
= Rs.P
10
According to question,
\ P 1+R
100FHG
IKJ
LNMM
OQPP
2
1– –P
10
= 132
Þ P 1+10100
FHG
IKJ
LNMM
OQPP
2
1– –P
10
= 132
Þ P1110
12F
HGIKJ
LNMM
OQPP– –
P10
= 132
Þ P121100
–1FHG
IKJ –
P10
= 132
Þ21P100
–P
10 = 132
Þ21P –10P
100 = 132
Þ11P100
= 132
Þ P =132 100´
11 = Rs 1200
41. (3) Using Rule 1,
Let the principal be Rs. P.
According to the question,
P 12
+FHG
IKJ
R100
– P 1 +FHG
IKJ
R100 = 420
ÞP 1 +FHG
IKJ
R100
1 1+FHG
IKJ
R100
– = 420
ÞP 1 +FHG
IKJ
R100
×R
100 = 420
ÞP 1 +FHG
IKJ
5100
×5
100= 420
ÞP 1 +FHG
IKJ
120 = 420 × 20
ÞP ×2120
= 420 × 20
ÞP =420 20 20´ ´
21 = Rs. 8000
42. (4) Using Rule 1,Time = T half–years
Rate =52
% per half year
SME–555
COMPOUND INTEREST
A = P 1100
+FHG
IKJ
R T
Þ 68921 = 64000 1200
+FHG
IKJ
5 T
Þ 6892164000
= 1140
+FHG
IKJ
T
Þ 6892164000
=4140
FHG
IKJ
T
Þ 4140
3FHG
IKJ =
4140
FHG
IKJ
T
Þ T = 3 half years
=32
112
= years
43. (4) Using Rule 1,A = P
1100
+FHG
IKJ
R T
Þ 12100 = P 110100
2
+FHG
IKJ
Þ 12100 = P1110
2FHG
IKJ
Þ 12100 = P ×121100
Þ P =12100 100
121´
= Rs. 10000
44. (4) Using Rule 1,
A = P 1R
100
T
+FHG
IKJ
Þ 1348.32 = 1200 1100
2
+FHG
IKJ
R
Þ1348 32
1200.
= 1100
2
+FHG
IKJ
R
Þ134832120000
= 1100
2
+FHG
IKJ
R
Þ1123610000
= 1100
2
+FHG
IKJ
R
Þ106100
12 2F
HGIKJ = +F
HGIKJ
R100
Þ106100
= 1100
+R
Þ 16
100+ = 1
100+
R
Þ R = 6% per annum.
45. (3) Using Rule 1,Rate of interest
=204
= 5% per quarter
Time = 3 quarters
\ C.I. = P 1100
1+FHG
IKJ
LNMM
OQPP
RT
–
= 12000 15
1001
3
+FHG
IKJ
LNMM
OQPP–
= 12000 1120
13
+FHG
IKJ
LNMM
OQPP–
= 120002120
13F
HGIKJ
LNMM
OQPP–
= 1200092618000
1–FHG
IKJ
=12000 1261
8000´
= Rs. 1891.5
46. (2) Amount= Rs. (30000 + 4347)= Rs. 34347
A = P 1R
100
T
+FHG
IKJ
Þ 34347 = 30000 17
100+F
HGIKJn
Þ3434730000
=107100FHG
IKJ
n
Þ1144910000
=107100FHG
IKJ
n
Þ107100
2FHG
IKJ =
107100FHG
IKJ
n
Þ n = 2 years47. (2) Let the principal be Rs. P.
\ A = P 1R
100
T
+FHG
IKJ
Þ 2420 = P 110100
2
+FHG
IKJ
Þ 2420 = P 110100
2
´ +FHG
IKJ
Þ 2420 = P1110
2FHG
IKJ
Þ P =2420 10 10
11 11´ ´´
= Rs. 2000
48. (3) Rate of interest =84
= 2%
per quarterTime = 3 quarters
C.I. = P 1R
100–1
T
+FHG
IKJ
LNMM
OQPP
= 5000 12
1001
3
+FHG
IKJ
LNMM
OQPP–
= 5000 102 13. –b gLNM OQP= 5000 (1.061208 –1)= 5000 × 0.061208= Rs. 306.04
49. (3) A = P 1R
100
T
+FHG
IKJ
Þ 800 = PR
1100
3
+FHG
IKJ ....(i)
and,
840 = PR
1100
4
+FHG
IKJ ....(ii)
On dividing equation (ii) by (i),
840800
1100
= +R
Þ2120
1100
= +R
ÞR
1002120
1120
= - =
Þ R =120
× 100
= 5% per annum50. (4) Rate = 10% Per annum
= 5% per half yearTime = T years = 2T half years
\ A = P 1+R
100
TFHG
IKJ
Þ 926.10 = 800 1+5
100FHG
IKJ
2T
Þ9261800
1120
.= +FHG
IKJ
2T
Þ92618000
2120
= FHG
IKJ
2T
Þ2120
2120
3 2FHG
IKJ = F
HGIKJ
T
Þ 2T = 3 Þ T =32
years
SME–556
COMPOUND INTEREST
51. (2) A = P 1R
100
T
+FHG
IKJ
Þ 4000 = 2000 1R
100
2
+FHG
IKJ
Þ 2 = 1R
100
2
+FHG
IKJ
Þ 1R
100+ = 2 ......(1)
\ 8000 = 2000 1R
100
T
+FHG
IKJ
Þ 4 = ( )2 T
Þ ( )2 4 = ( )2 T
Þ T = 4 years
52. (3) A = P 1+R
100
TFHG
IKJ
= 64000 1+7.5100
FHG
IKJ
3
= 64000 13
40
3
+FHG
IKJ
= 640004340
3FHG
IKJ
=64000 43 43 43
40 40 40´ ´ ´´ ´
= Rs. 79507\ C.I. = Rs. (79507 – 64000)= Rs. 15507
53. (3) Principal = Rs. 4096
Time =32
years = 3 half years
Rate =252
% per annum
=254
% per half year
\ A = P 1R
100
T
+FHG
IKJ
= 4096 125400
3
+FHG
IKJ
= 4096 11
16
3
+FHG
IKJ
= 4096 ×1716
1716
1716
´ ´
= Rs. 4913
54. (3) A = P 1R
100
T
+FHG
IKJ
Þ 11664 = 10000 1R
100
2
+FHG
IKJ
Þ 1166410000
= 1R
100
2
+FHG
IKJ
Þ 108100
2FHG
IKJ = 1
R100
2
+FHG
IKJ
Þ 1R
100+ =
108100
Þ R
100 =
108100
–1 =8
100
\ R =8
100100´
= 8% per annum
55. (1) C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
= 4000 110
1001
4
+FHG
IKJ
LNMM
OQPP–
= 40001110
14F
HGIKJ
LNMM
OQPP–
= 4000 (1.4641 – 1)= 4000 × 0.4641 = Rs. 1856.4
56. (2) A = P 1R
100
T
+FHG
IKJ
\ 2420 = P 1R
100
2
+FHG
IKJ .... (i)
and, 2662 = P 1R
100
3
+FHG
IKJ .. (ii)
By equation (ii) ÷ (i)
26622420
= 1 +R
100
ÞR
100 =
26622420
– 1
=2662 2420
2420–
ÞR
100 =
2422420
=1
10Þ R = 10% per annum.From equation (i),
2420 = P 1+10100
FHG
IKJ2
Þ 2420 = P1110
2FHG
IKJ
Þ 2420 = P ×121100
Þ P =2420 100
121´
= Rs. 2000
57. (1) A = P 1R
100
T
+FHG
IKJ
Þ 6000 = 3000 1R
100
2
+FHG
IKJ
Þ 2 = 1R
100
2
+FHG
IKJ
On squaring,
4 = 1R
100
4
+FHG
IKJ
i.e. Amount= Rs. (4 × 3000)= Rs. 12000
\ C.I. = Rs. (12000 – 3000)= Rs. 9000
58. (3) Rate of interest= 12% per annum= 6% per half–yearTime = 2 half years
\ C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
= 12500 16
1001
2
+FHG
IKJ
LNMM
OQPP–
= 12500 13
501
2
+FHG
IKJ
LNMM
OQPP–
= 125005350
12F
HGIKJ
LNMM
OQPP–
= 1250028092500
1–FHG
IKJ
= Rs.12500 309
2500´F
HGIKJ
= Rs. 154559. (1) Let the principal be Rs. P.
A = PR
T
1100
+FHG
IKJ
Þ 6655 = P 110100
3
+FHG
IKJ
Þ 6655 = P 11
10
3
+FHG
IKJ
Þ 6655 = P1110
3FHG
IKJ
Þ P =6655 10 10 10
11 11 11´ ´ ´´ ´
= Rs. 5000
SME–557
COMPOUND INTEREST
60. (1) Let the time be T years.
\ A = P 1+R
100
TFHG
IKJ
Þ 9261 = 8000 1+5
100
TFHG
IKJ
Þ92618000
= 1120
T
+FHG
IKJ
Þ2120
3FHG
IKJ =
2120
TFHG
IKJ
Þ T = 3 years
61. (2) C.I. = PR
T
1100
1+FHG
IKJ -
LNMM
OQPP
= 1000 110100
13
+FHG
IKJ -
LNMM
OQPP
= 1000 11
101
3
+FHG
IKJ -
LNMM
OQPP
= 10001110
13F
HGIKJ -
LNMM
OQPP
= 100013311000
1-FHG
IKJ
=1000 331
1000´
= Rs. 331
62. (2) C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
= 25000 15
1001
2
+FHG
IKJ
LNMM
OQPP–
= 25000 1120
12
+FHG
IKJ
LNMM
OQPP–
= 25000441400
1–FHG
IKJ
= 2500441– 400
400FHG
IKJ
=25000 41
400´
= Rs. 2562.5
63. (1) Rate = 10% per annum= 5% per half year
Time = 112
years = 3 half years
\ C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
= 24000 15
1001
3
+FHG
IKJ
LNMM
OQPP–
= 24000 1120
13
+FHG
IKJ
LNMM
OQPP–
= 240002120
13F
HGIKJ
LNMM
OQPP–
= 2400092618000
1–FHG
IKJ
=24000 1261
8000´
= Rs. 3783
64. (1) C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
Þ 3225 = P 115
1001
2
+FHG
IKJ
LNMM
OQPP–
Þ 3225 = P 13
201
2
+FHG
IKJ
LNMM
OQPP–
Þ 3225 = P2320
12F
HGIKJ
LNMM
OQPP–
Þ 3225 = P529400
1–FHG
IKJ
Þ 3225 = P529 400
400–F
HGIKJ
Þ 3225 = P ×129400
Þ P =3225 400
129´
= Rs. 10000
65. (1) A = P 1R
100
T
+FHG
IKJ
Þ 3993 = 3000 1100
3
+FHG
IKJ
x
Þ39933000
= 1100
3
+FHG
IKJ
x
Þ13311000
= 1100
3
+FHG
IKJ
x
Þ1110
3FHG
IKJ = 1
100
3
+FHG
IKJ
x
Þ 1 +x
100 =
1110
Þx
100 =
1110
– 1 =1
10
Þ x =1
10 × 100
= 10% per annum
66. (2) A = P 1+R
100
TFHG
IKJ
Þ 2P = P 1+19100
TFHG
IKJ
Þ 2 =119100
TFHG
IKJ
Þ 2 = (1.19)T
If T = 4 years,(1.19)4 > 2
TYPE-II
1. (3) Let the sum be P.
\ = +FHG
IKJ
LNMM
OQPP101 50 1
3100
12
. –P
QC I Pr n
. . –= +FHG
IKJ
LNMM
OQPP
LNMM
OQPP1
1001
Þ = FHG
IKJ
LNMM
OQPP10150
103100
12
. –P
= FHG
IKJP
10609 1000010000
–
Þ P =10150 10000
609. ´
=1015000
609
\ S.I. =´ ´
´1015000 2 3
609 100= 100
Aliter : Using Rule 10,Here, C.I. = Rs 101.50R = 3%, S.I. = ?
C.I. = S.I. 1200
+FHG
IKJ
R
101.50 = S.I. 13
200+F
HGIKJ
S.I. =10150 200
203. ´
S.I. = 1002. (2) Using Rule 1,
Suppose principal be x
Þ x 15
1001 252 20
3
+FHG
IKJ -
RS|T|
UV|W|
= .
Þ x2120
1 252 203F
HGIKJ -
RS|T|
UV|W|
= .
Þ´ ´ - ´ ´
´ ´RST
UVW =x21 21 21 20 20 20
20 20 2025220.
SME–558
COMPOUND INTEREST
Þ x12618000
252 20= .
\ x =× ´
=252 20 8000
12611600
Þ SI =´ ´1600 5 3
100 = 240
3. (3) Using Rule 10,If SI on a certain sum for twoyears is x and CI is y, then
y xr
= +FHG
IKJ1
200
Þ28215 270 1100
. = +FHG
IKJ
r
Þ 1200
28215270
+ =r .
Þr
20028215
2701= -
.
Þr
2001215270
=.
Þ r =´
=1215 200
2709%
.
4. (2) C.I. = +FHG
IKJ
LNMM
OQPPP 1
R100
– 1T
Þ = +FHG
IKJ
LNMM
OQPP510 1
25200
12
P –
Þ = FHG
IKJ510
8164
1P –
Þ =´
=P510 64
171920
\ S.I. =´ ´
´1920 2 25
100 2= 480
Aliter : Using Rule 10,Here, C.I. = 510
R = 1212
%, S.I. = ?
C.I. = S.I. 1200
+FHG
IKJ
R
510 = S.I. 125400
+FHG
IKJ
S.I. =510 400
425´
S.I. = 4805. (3) Let the principal be P and rate
of interest be r per cent per an-num. Then,
C. I = P 1100
12
+FHG
IKJ -
LNMM
OQPP
r
Þ 40.80 = P 1100
12
+FHG
IKJ -
LNMM
OQPP
r....(i)
S.I. =P.r.t100
Þ 40 =Pr 2100
´ ...(ii)
\40 80
40.
=
P
2Pr100
1100
12
+FHG
IKJ -
LNMM
OQPP
r
Þ 1.02
=1002r
110000
2100
12
+ + -LNMM
OQPP
r r
Þ 1.02 =r
200+1
Þr
200 = 1.02 – 1
Þ r = 0.02 × 200\ r = 4% per annum.Aliter : Using Rule 10,Here, C.I. = 40.80S.I. = 40, R = ?
C.I.= S.I. 1200
+FHG
IKJ
R
40.80 = 40 1200
+FHG
IKJ
R
40804000
= 1200
+R
408400
=200
200+ R
408 = 400 + 2R 2R = 8 R = 4%
6. (1) Let the principal be P.
\ C.I. = P 1 1+FHG
IKJ -
LNMM
OQPP
R100
T
Þ 328 = P 1 1+FHG
IKJ -
LNMM
OQPP
5100
2
Þ 328 = P441400
1-LNM
OQP
Þ 328 = P441 400
400-L
NMOQP
Þ P =328 400
41´
= 3200
\ S.I.
=PRT100
=´ ´3200 5 2
100 = 320
Aliter : Using Rule 10,Here, C.I. = 328,R = 5%, S.I. = ?
C.I.= S.I. 1200
+FHG
IKJ
R
328 = S.I. 15
200+F
HGIKJ
328 = S.I. 1140
+FHG
IKJ
S.I. =328 40
41´
S.I. = 8 x 40 = 320
7. (2) C.I.= P 1+100
Pr tF
HGIKJ -
2448 = P 1100
1+FHG
IKJ -
LNMM
OQPP
r t
or 2448 = P 14
1001
2+F
HGIKJ -
LNMM
OQPP
Þ 2448 = P676625
1-LNM
OQP
2448 = P51
625LNM
OQP
\ P =2448 625
51´
P = 30,000
\ S.I. =30000 4 2
100´ ´
= 2400
Aliter : Using Rule 10,Here, C.I. = 2448R = 4%, S.I. = ?
C.I.= S.I. 1200
+FHG
IKJ
R
2448 = S.I. 14
200+F
HGIKJ
2448 = S.I. 1150
+FHG
IKJ
2448 = S.I.5150
FHG
IKJ
S.I. =2448 50
51´
S.I. = 24008. (3) Using Rule 1,
Let the principal be x and rate ofinterest be r% per annum.Now,
S.I. =Principal Time Rate
100´ ´
SME–559
COMPOUND INTEREST
260 =x r´100 ....(i)
C.I.= P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
540.80 = x 1100
12
+FHG
IKJ -
LNMM
OQPP
r
Þ 540.80 = x 12
100 100001
2+ + -
LNMM
OQPP
r r
Þ 540.80 =2100 10000
2xr xr+
Þ 540.80 = 2 × 260 +260100
.r
Þ 260r = 54080 – 52000Þ 260r = 2080
Þ r =2080260
8= %
9. (4) Principal =S.I. 100
Time Rate´´
=80 100
2 4´´
= 1000
\ C.I. = P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
= 1000 14
1001
2
+FHG
IKJ -
LNMM
OQPP
= 10002625
12F
HGIKJ -
LNMM
OQPP
= 1000676625
1-FHG
IKJ
= 1000676 625
625-F
HGIKJ
=1000 51
625´
= 81.60
Aliter : Using Rule 10,Here, S.I. = 80R = 4%, C.I. = ?
C.I.= S.I. 1200
+FHG
IKJ
R
C.I.= 80 14
200+F
HGIKJ
= 80 1150
+FHG
IKJ
= 80 ×5150
= 81.60
10. (4) Using Rule 1,
C.I. = P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
246 = P 15
1001
2
+FHG
IKJ -
LNMM
OQPP
Þ 246 = P2120
12F
HGIKJ -
LNMM
OQPP
Þ 246 = P441 400
400-F
HGIKJ
Þ 246 =41P400
Þ P =246 400
41´
= 2400
\ SI =Principal Time Rate
100´ ´
=2400 3 6
100´ ´
= 432
11. (4) Difference of CI and SI for twoyears= (954 – 900) = 54\ Sum= Difference in CI and SI
×100Rate
2FHG
IKJ
Rate =2 Difference 100
Simple interest´ ´
=2 5400
90012%
´=
\ Sum = 5410012
2´FHG
IKJ
= 54253
253
´ ´ = 3750
Aliter : Using Rule 10,C.I. = Rs. 954, S.I.=Rs. 900, P=?
C.I.= S.I. 1200
+FHG
IKJ
R
954 = 900 1200
+FHG
IKJ
R
954900
= 1200
+R
954900
1- =R
200
954 900900
-=
R200
549
=R2
R = 12%
Now S.I. =P R T´ ´
100
900 =P ´ ´12 2
100P = Rs. 3750
12. (4) If the principal be P then
C.I. = P 1100
1+FHG
IKJ -
LNMM
OQPP
RT
Þ 420 = P 110100
12
+FHG
IKJ -
LNMM
OQPP
Þ 420 = P121 100
100-F
HGIKJ
Þ 420 =P100´ 21
Þ P =420 100
21´
= 2000
\ S.I. =PRT100
=2000 10 2
100´ ´
= 400
Aliter : Using Rule 10,Here, C.I. = Rs. 420,R = 10%, S.I. = ?
C.I. = S.I. 1200
+FHG
IKJ
R
420 = S.I. 110200
+FHG
IKJ
420 = S.I.210200
FHG
IKJ
S.I. =420 200
210´
S.I. = Rs. 400
13. (4) If the sum be P, then
C.I. = P 1100
1+FHG
IKJ -
LNMM
OQPP
R T
Þ 102 12
= FHG
IKJ -
LNMM
OQPPP 1+
4100
SME–560
COMPOUND INTEREST
Þ 102 12
= FHG
IKJ -
LNMM
OQPPP
2625
Þ 102 1= -FHG
IKJP
676625
Þ 102 = FHG
IKJP
676 – 625625
Þ 102 = ´P51
625
Þ P =102 625
51´
= 1250
\ S.I. =1250 2 4
100´ ´
= 100
14. (4) Using Rule 1,Let S.I. = 100,& Principal = 100
\ Rate =S.I. 100
Principal Time´
´
=100 100100 8
´´
=252
%
\ C.I. = PT
1100
1+FHG
IKJ -
LNMM
OQPP
r
= 8000 125200
1+FHG
IKJ -
LNMM
OQPP
2
= -FHG
IKJ8000
8164
1 =´8000 17
64
= 2125
15. (1) C.I. = P 1 1+FHG
IKJ
LNMM
OQPP
R100
T
–
Þ 2544 = P 1+12100
FHG
IKJ
LNMM
OQPP
2
1–
Þ 2544 = P2825
FHG
IKJ
LNMM
OQPP
2
1–
Þ 2544 = P784625
1–FHG
IKJ
Þ 2544 = P784 625
625–F
HGIKJ
2544 =P 159
625´
Þ P =2544 625
159´
= 10000
\ S.I. =P R T
100´ ´
=10000 2 12
100´ ´
= 2400
Aliter : Using Rule 10,Here, C.I. = Rs. 2544R = 12%, S.I. = ?
C.I. = S.I. 1200
+FHG
IKJ
R
2544 = S.I. 112200
+FHG
IKJ
2544 = S.I.212200
FHG
IKJ
S.I. =2544 200
212´
= 2400
16. (2) Using Rule 1,
A = P 1R
100
T
+FHG
IKJ
Þ 2916 18
100
2
= +FHG
IKJx
Þ 29162725
2
= FHG
IKJx
Þ x =2916 25 25
27 27´ ´
´= 2500
\ S.I. =P × R × T
100
=2500 9 3
100´ ´
= 675
17. (1) Using Rule 6,S.I. for 3 years = 3000
S.I. for 2 years =3000
32´
= 2000C.I. – S.I.= 2050 – 2000 = 50
S.I. =PR 3100
´
Þ PR =3000 100
3´
= 100000
\ Difference =P R10000
2´
Þ 50 =P (100000)
10000 P
2
2´
´
Þ P =1000000
50 = 20000
18. (1) Compound interest
= P 1100
1+FHG
IKJ -
LNMM
OQPP
RT
Þ 410 = P 15
1001
2
+FHG
IKJ -
LNMM
OQPP
Þ 410 = P 1120
12
+FHG
IKJ -
LNMM
OQPP
Þ 410 = P2120
12F
HGIKJ -
LNMM
OQPP
Þ 410 = P441400
1-FHG
IKJ
Þ 410 = P41
400FHG
IKJ
Þ P =410 400
41´
= 4000
\ S.I.
=Principal Time Rate
100´ ´
=4000 2 5
100´ ´
= 400
Aliter : Using Rule 10,Here, C.I. = Rs. 410R = 5%, S.I. = ?
C.I. = S.I. 1200
+FHG
IKJ
R
410 = S.I. 15
200+F
HGIKJ
410 = S.I.205200
FHG
IKJ
S.I. =410 200
205´
S.I. = Rs.400
19. (4) Principal = P (let)
\ C.I. = P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
Þ 510 = P 125200
12
+FHG
IKJ -
LNMM
OQPP
SME–561
COMPOUND INTEREST
Þ 510 = P 118
12
+FHG
IKJ -
LNMM
OQPP
Þ 510 = P98
12F
HGIKJ -
LNMM
OQPP
Þ 510 = P8164
1-FHG
IKJ
Þ 510 = P81 64
64-F
HGIKJ
Þ 510 =17P64
Þ P =510 64´
17 = 1920
\ S.I.
=Principal Time Rate
100´ ´
=1920 2 25
100 2´ ´
´ = 480
Aliter : Using Rule 10,Here, C.I. = 510
R = 1212
%, S.I. = ?
C.I. = S.I. 1200
+FHG
IKJ
R
510 = S.I. 125400
+FHG
IKJ
510 = S.I.425400
FHG
IKJ
S.I. =510 400
425´
S.I. = 48020. (2) Using Rule 1,
Sum borrowed = Rs. x
\ Simple interest after 4 years
=x ´ ´4 5
100 = Rs.
x
5Amount lent of on compoundinterest
= Rs.x
2
\ C.I. = P 1R
1001
T
+FHG
IKJ -
LNMM
OQPP
=x
21
10100
14
+FHG
IKJ -
LNMM
OQPP
=x
21 1 14.b g -
=x
2 (1.4641 – 1)
= Rs.0 4641
2. x
\0 4641
2 5. x x
- = 3205
Þ2 3205 2
10. x x-
= 3205
Þ 0.3205x = 32050
Þ x =320500 3205.
= Rs. 100000
21. (3) S.I. for 2 years
=23
× 540 = Rs. 360
C.I. – S.I.= 376.20 – 360 = Rs. 16.20\ Rate of interest
=16 20180
. × 100
= 9% per annum
\ Principal =S.I. 100
Time Rate´´
=180 100
1 9´´ = Rs. 2000
22. (2) Principal =S.I. 100
Time Rate´´
=350 100
2 4´´ = Rs. 4375
Difference =PR2
10000
=4375 4 4
10000´ ´
= Rs. 723. (3) Q S.I. for 3 years
= Rs. 240
\ S.I. for 2 years =2403
2´
= Rs. 160
\PR 2100
´ = 160
Þ PR = 160 × 50 = 8000...(i)
Again, C.I. – S.I.= 170 – 160 = Rs. 10
ÞPR
10000
2
= 10
Þ8000 R10000
´ = 10
Þ R =100
8 =
252
= 1212
%
24. (2) Principal =S.I. 100
Time Rate´´
=1600 100
5 2´
´ = Rs. 16000
C.I. = P 1R
100–1
T
+FHG
IKJ
LNMM
OQPP
= 16000 15
100–1
3
+FHG
IKJ
LNMM
OQPP
= 160002120
FHG
IKJ
LNMM
OQPP
3
–1
= 1600092618000
1–FHG
IKJ
=16000 1261
8000´
= Rs. 2522
25. (4) Let the principal be Rs. P.For 4 years,
S.I. =Principal Time Rate´ ´
100
=P 4 5
100´ ´
= Rs.P5
C.I. = P 1+R
100– 1
TFHG
IKJ
LNMM
OQPP
= P 1+10
100FHG
IKJ
LNMM
OQPP
4
1–
= P1110
14F
HGIKJ
LNMM
OQPP–
= P1464110000
1–FHG
IKJ
=4641P10000
According to the question,
4641P10000
–P5
= 26410
Þ4641P – 2000P
10000 = 2641
Þ2641P10000
= 2641
Þ P = Rs. 10000
SME–562
COMPOUND INTEREST
26. (2) Principal =S.I. 100
Time Rate´´
=50 100
2 5´´
= Rs. 500
\ C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
= 500 15
1001
2
+FHG
IKJ
LNMM
OQPP–
= 500 1120
12
+FHG
IKJ
LNMM
OQPP–
= 5002120
12F
HGIKJ
LNMM
OQPP–
= 500441400
1–FHG
IKJ
=500 41
400´
= Rs. 51.25
27. (4) According to the question,If principal= Rs. 100 then interest= Rs. 40.
\ Rate =S.I. 100
Principal Time´
´
=40 100100 8
´´ = 5% per annum
Case II.
\ A = P 1R
100
T
+FHG
IKJ
= 30000 15
100
2
+FHG
IKJ
= 30000 1120
2
+FHG
IKJ
= 3000020 1
20
2+FHG
IKJ
= 30000 ×2120
2120
´
= Rs. 33075
\ C. I. = Rs. (33075 – 30000)
= Rs. 3075
TYPE-III
1. (1) TRICK As the interest was compounded
half-yearly, we changed r tor2
and t to 2t.\ T = 1 year & R 6%Sum
=´ ´
´36 100 100
6 6= 10000
2. (2) Compound Interest (whencompounded yearly)
= +FHG
IKJ5000 1 4
1005000
15.–
= FHG
IKJ5000
2625
500015.
–
= 5302.9805 – 5000 = 302.9805C.I. (When compounded half-yearly).
= +FHG
IKJ5000 1 2
10050000
3–
= 5306.04 – 5000 = 306.04Required difference= (306.04 – 302.9805)= 3.059 = 3.06
3. (3) Let the sum x. Then,
C.I. = +FHG
IKJx x1
5100
2
–
= - =441x400
x441x – 400x
400
=41
400x
Now,
S.I. =´ ´
=x x5 2
100 10
\ (C.I.) – (S.I.)=41400 10
x x–
= =41 40
400 400x x x–
\ =x
40015
Þ x = 15 × 400 = 6000Hence, the sum is 6000Aliter : Using Rule 6,C.I. – S.I. = 15, R = 5%, T = 2years, P =?
C.I. – S.I. = PR
100
2FHG
IKJ
15 = P5
100
2FHG
IKJ
P = 15 × 400
P = 60004. (4) Tricky Approach
Difference of SI and CI for 3 years
=PR(300 R)
1003+
QP ´ ´
´ ´25 305
100 100 100= 36.60
Þ =´ ´ ´
´P
36 60 100 100 10025 305
.
= 4800Aliter : Using Rule 6,C.I.–S.I. = 36.60, R = 5%, P =?,T = 3yrs.
C.I. – S.I.= PR R
1003
100
2FHG
IKJ ´ +
FHG
IKJ
36.60 = P5
1003
5100
2FHG
IKJ ´ +
FHG
IKJ
36.60 = P ×25
100
3051002
´
P =36 60 100 100 100
25 305. ´ ´ ´
´
P =3660000025 305´
= 4800
5. (4) S.I. =´ ´2500 2 4
100= 200
C.I. = +FHG
IKJ
LNMM
OQPP–2500 1
4100
12
=FHG
IKJ
LNMM
OQPP–2500
2625
12
=676 625
6252500
–b g´
= ´51
6252500 = 204
\ The required difference= C.I. – S.I. = (204 – 200) = 4Aliter : Using Rule 6,Here, C.I. – S.I.= ?, P = 2500R = 4%, T = 2
SME–563
COMPOUND INTEREST
C.I. – S.I.= PR
100
2FHG
IKJ
= 25004
100
2FHG
IKJ
= 2500 ´125
´125
C.I.–S.I. = 46. (4) Let the sum be x. Then,
C.I. = +FHG
IKJx x1
10100
2
– =21100
x
S.I. =´ ´
=x x10 2
100 5
\ C.I. – S.I. = =21100 5 100
x x x–
Given that, =x
10065
\ x = 6500Hence, the sum is 6500.Aliter : Using Rule 6,Here, C.I. – S.I. = 65,R = 10%, T = 2 years, P = ?
C.I. – S.I. = PR
100
2FHG
IKJ
65 = P10100
2FHG
IKJ
P = 65007. (3) When difference between the
compound interest and simpleinterest on a certain sum of mon-ey for 2 years at r% rate is x, then
x = Sumr
100
2FHG
IKJ
Þ 10 = 1000r
100
2FHG
IKJ
Þr
100
2FHG
IKJ =
101000
Þr
100 =
1100
=1
10
Þ r =10010
= 10%
Aliter : Using Rule 6,Here, C.I. – S.I. = Rs. 10R = ?, T= 2 years, P = Rs. 1000
C.I. – S.I. = PR
100
2FHG
IKJ
10 = 1000R
100
2FHG
IKJ
10 = 1000 ´R
100´
R100
Þ R2 = 100
Þ R = 100 = 10%
8. (2) Using Rule 6,When difference between the com-pound interest and simple inter-est on a certain sum of money for2 years at r % rate is x, then thesum is given by
xr
100 2FHG
IKJ Here x = 80,
r = 40%
\ Required sum = 80100
4
2FHG
IKJ
= 80 × 25 × 25 = 500009. (2) Using Rule 6,
When difference between the CIand SI on a certain sum of moneyfor 2 years at r % rate is x, then
Sum = x ×100 2
rFHG
IKJ
= 1 ×100
4
2FHG
IKJ = 625
10. (1) Using Rule 6,
Sum = Difference100 2
rFHG
IKJ
= 4 ×100
4
2FHG
IKJ = 2500
11. (1) Using Rule 6,Difference between C.I. and S.Ifor 3 years
=PR
100
R100
32
2b g+F
HGIKJ
Þ =´
+FHG
IKJ15.25
P 2510000
5100
3
Þ =´
´15.25
P 305400 100
Þ =´ ´
P15.25 400 100
305
= 2000
12. (3) Using Rule 6,Tricky Approach
Sum = (CI – SI)100 2
rFHG
IKJ
= 768 ×100
8
2FHG
IKJ = 1,20,000
13. (3) Using Rule 6 and 1,If the difference between com-pound interest and simple inter-est at the rate of r% per annumfor 2 years be x, then
Principal = x100 2
r
FHG
IKJ
= 2810010
2FHG
IKJ = 2800
If the interest is compounded halfyearly, then
r =102
= 5%,
Time = 4 half years
Simple interest =2800 5 4
100´ ´
= 560Compound interest
= 2800 15
1001
4
+FHG
IKJ
LNMM
OQPP–
= 2800 [1.2155 – 1]= 2800 × 0.2155 = 603.41\ Difference = (603.41–560)= 43.41
14. (3) Using Rule 1,C.I. after 3 years
= 6000 15
1001
3
+FHG
IKJ
LNMM
OQPP–
= 60009261 8000
8000–F
HGIKJ
= 6000 ×12618000
= 945.75
CI after 2 years
= 6000 15
1001
2
+FHG
IKJ
LNMM
OQPP–
= 6000441 400
400–F
HGIKJ
= 6000 ×41400
= 615
Required difference= (945.75 – 615) = 330.75
SME–564
COMPOUND INTEREST
15. (1) Let the principal be x.Compound interest
= P 1R
100–1
t
+FHG
IKJ
LNMM
OQPP
= x 110100
–12
+FHG
IKJ
LNMM
OQPP
= x [(1.1)2 – 1]= x (1.21 – 1) = 0.21x
SI =x ´ ´2 10
100 =
x
5= 0.2x
According to the question,0.21x – 0.2x = 40Þ 0.01x = 40
Þ x =40
0 01. = 4000
Aliter : Using Rule 6,Here, C.I. – S.I. = 40R = 10%, T = 2 years, P = ?
C.I. – S.I. = PR
100
2FHG
IKJ
40 = P10100
2FHG
IKJ
P = 400016. (1) Using Rule 6,
Let the difference between CI andSI on a certain sum for 3 years atr % be x,then the sum
=´
+
Difference ( )
( )
100
300
3
2r r
=´
+122 10025 300 5
3
( )
=´
12200000025 305
= 16000
17. (2) Using Rule 6,Difference of two years
= Pr2
10000
FHG
IKJ
Þ 48 = P400
10000FHG
IKJ
Þ 48 =P
25Þ P = 48 × 25 = 1200
18. (1) Using Rule 6,
Difference =PR2
10000
Þ =´
2510000
10000
2R
Þ R = 5%19. (2) Using Rule 6,
Difference =P r2
10000
Þ =´ ´
65 5
10000P
Þ P = 6 × 400 = 240020. (3) Using Rule 6,
Rate of interest = 8% per half-yearTime = 2 half years
Difference of interests =PR2
100
Þ 56 =P (8)
(100)
2
2´
Þ P =56 10000
64´
= 8750
21. (4) Let the sum be xr = 10%, n = 3 years
S.I. =´ ´x r n100
S.I.=´ ´
=x x10 3
1003
10
C.I.= +FH
IK
LNMM
OQPP1
1001r x
n–
= +FH
IK
LNMM
OQPP1 10
1001
3– x
= FH
IK
LNMM
OQPP
1110
13
– x
= FH
IK
13311000
1– x =331
1000x
3311000
310
31x x– =
or331 300
100031–a f x =
or31
100031x =
or x = 1000
\ Sum = 1000Aliter : Using Rule 6,Here, C.I. – S.I. = 31R = 10%, T = 3 years, P = ?C.I. – S.I.
= P ×R
100
2FHG
IKJ × 3
100+F
HGIKJ
R
31 = P ×10100
2FHG
IKJ 3
10100
+FHG
IKJ
31 = P ´1
100´
3110
P = 100022. (4) Using Rule 6,
Let the sum be x.When difference between the com-pound interest and simple interest ona certain sum of money for 2 years atr% rate isx, then the sum is given by:
Sum = Difference ×100Rate
2FHG
IKJ
= 8100
4´ FHG
IKJ2
= 8 × 25 × 25 = 500023. (2) If the interest is compounded
half yearly,
C.I. = PR
T
1100
1+FHG
IKJ -
LNMM
OQPP
= P5
2
1100
1+FHG
IKJ -
LNMM
OQPP
= P21
2
201
FHG
IKJ -
LNMM
OQPP =
41P400
S.I. =P R T
100´ ´
=P100´10
=P
10
\41P400
P- =
10180
Þ 41P 40P
400-
= 180
ÞP
400= 180
Þ P = 72000Aliter : Using Rule 6,Here, C.I. – S.I. = 180Interest is compounded halfyearly
R =105
= 5%,
T = 2 years
C.I. – S.I. = PR
100
2FHG
IKJ
SME–565
COMPOUND INTEREST
Þ 180 = P5
100
2FHG
IKJ
Þ P = 180 × 20 × 20
P = 7200024.(1) Using Rule 6,
Difference =PR
(100)
2
2
Þ 1.50 =P 5 5
(100)2´ ´
Þ P = 400 × 1.5 = 60025. (3) Using Rule 6,
Time =32
2 3´ = half years
Rate =102
= 5% per half year
[Q when r ® r/2, then t ® 2t]Difference
= Pr r3 2
10000003
10000+
FHG
IKJ
Þ 244 = P125
100000075
10000+F
HGIKJ
Þ 244 = P7625
1000000FHG
IKJ
Þ P =244 1000000
7625´
= 3200026. (3) Using Rule 6,
The difference between compoundinterest and simple interest fortwo years
= Principal Rate
100 100
2´´
b g
\ 1 =´Principal 4
10000
2b g
Þ Principal =10000
16= 625
27. (2) Using Rule 6,Difference of 2 years
=p r´ 2
10000
Þ 325000
10000
2
=´ r
Þ r2 32 100005000
64=´
=
Þ r = 64 8%=28. (1) Using Rule 6,
Difference =PR2
10000
Þ 25 =P 5 5´ ´10000
Þ P = 1000029. (3) Using Rule 6,
Difference =PR
10000
2
Þ 300 =P 10´ ´10
10000
Þ P = 300 × 100 = 3000030. (1) Using Rule 1,
S.I. =Principal Time Rate
100´ ´
=32000 4 10
100´ ´
= 12800
C.I. = P 1R
1001
4
+FHG
IKJ -
LNMM
OQPP
= 32000 110
1001
4
+FHG
IKJ -
LNMM
OQPP
= 32000 [(1.1)4 – 1]= 32000 (1.4641 – 1)
= 32000 × 0.4641= 14851.2
\ Required difference
= 14851.2 – 12800 = 2051.231. (3) Using Rule 6,
Difference =PR
10000
2
Þ 63 =P 5 510000
´ ´
Þ P = 400 × 63 = 2520032. (4) Let the principal be Rs. P.
For 2 years
C.I. – S.I. =PR
10000
2
Þ 1 =P 4 4´ ´10000
Þ P =100004 4´
= Rs. 625
33. (1) Difference =PR2
10000
Þ 4 =P ´ ´10 10
10000
Þ P = Rs. 40034. (1) Difference between C.I. and
S.I. for 3 years
=Pr ( )2 3001000000
r +
Þ 93 =P ´ +100 10 300
1000000( )
Þ 93 =P ´ ´100 310
1000000
Þ31
100093
P=
Þ P =93000
31 = Rs. 3000
35. (3) Difference
=PR
10000
2
Þ 41 =P ´ ´5 510000
Þ 41 =P
400
Þ P = 41 × 400 = Rs. 1640036. (4) For 3 years,
C.I. – S.I.
= Pr
100
2FHG
IKJ
r
1003+F
HGIKJ
Þ P10100
2FHG
IKJ
10100
3+FHG
IKJ = 186
Þ P1
100FHG
IKJ ×
3110
= 186
Þ P =186 1000
31´
= Rs. 6000
37. (2) Difference between C.I. andS.I. for 3 years
= Pr r
100 1003
2FHG
IKJ +F
HGIKJ
= 400008
100
2FHG
IKJ
8100
3+FHG
IKJ
SME–566
COMPOUND INTEREST
= 40000 ×64
10000
8 300100+F
HGIKJ
= 4 × 64 ×308100
=78848100
= Rs. 788.48
38. (3) For 2 years,
C.I. – S.I. =PR2
10000
Þ 96 =15000
10000
2´ R
Þ 15 R2 = 960
Þ R2 =96015
= 64
Þ R = 64 = 8% per annum
39. (4) For 2 years,
C.I. – S.I. =PR
10000
2
=5000 8 8´ ´
10000 = Rs. 32
40. (4) For 2 years,
C.I. – S.I. =PR
10000
2
Þ 20 =P 5 5´ ´10000
ÞP
400 = 20
Þ P = Rs. (20 × 400)= Rs. 8000
TYPE-IV
1. (4) Suppose P = 100and amount A = 225
A Pr t
= +FHG
IKJ1
100
or 225 100 1100
2
= +FHG
IKJ
r
or225100
1100
2= +LNM
OQP
r
or 1100
1510
+ =r
or100
1001510
+=
r
or 100 + r = 150or r = 50%Aliter : Using Rule 8,Here, n = 2.25, t = 2 years
R% = n t1
1 100%-FHGG
IKJJ ´
R% = 2 25 1 100%12.b g -
LNMM
OQPP
´
= 15 1 100%. - ´
= 05 100%. ´= 50%
2. (2) A sum of x becomes 2x in4 years.Similarly, 2x will become 2 × 2x= 4x in next 4 years and 4xwill become 2 × 4x = 8x in yetanother 4 years. So, the total time= 4 + 4 + 4 = 12 yearsAliter : Using Rule 5,Here, m = 2, t = 4Time taken to become23 = n × t years
= 3 × 4 = 12 yearsNote : If a sum of money becomesn times in t years, it will becomet1 = nx times at the same rate ofinterest in t1 years given by,
3. (2) Let the sum be x which be-comes 2x in 10 years. Hence, 4xin 20 yearsMethod 2 :Unitary Method can also be used.Aliter : Using Rule 5,Here, m = 2, t = 10Time taken to become 4 times =22 times= t × n = 10 × 2 = 20 years
4. (1) Let the principal be x and therate of compound interest be r%per annum. Then,
8x = +FHG
IKJx
r1
100
3
Þ 8 1100
2 1100
33
3= +FHG
IKJ Þ = +F
HGIKJ
r r
Þ 2 = +1100
r
Þr
r100
1 100%= Þ =
Aliter : Using Rule 8,Here, n = 8, t = 3 years.
R% = n t1
1 100%-FHGG
IKJJ ´
= 8 1 100%13b g -
LNMM
OQPP
´
= 2 1 100%313e j -
LNMM
OQPP ´
= 100%5. (3) Let the sum be x.
Then,
2x = xr
1100
6
+FHG
IKJ
Þ 2 = 1100
6
+FHG
IKJ
r
Cubing both sides,
8 = 1100
6 3
+FHG
IKJ
RS|T|
UV|W|
r
Þ 8 = 1100
18
+FHG
IKJ
r
Þ 8x = xr
1100
18
+FHG
IKJ
\ The sum will be 8 times in 18years. i.e., Time = 18 yearsAliter : Using Rule 5,Here, m = 2, t = 6 yearsIt will becomes 8 times of itself= 23 times of it selfin t × n years = 6 × 3 = 18 years
6. (2) Let the Principal be P and rateof interest be r%.
\ 2 P = P 1100
2
+FHG
IKJ
r
Þ = +FHG
IKJ2 1
100
5r
...(i)
On cubing both sides,
8 = 1100
15
+FHG
IKJ
r
\ Time = 15 yearsAliter : Using Rule 5,Here, m = 2, t = 5 yearsIt becomes 8 times = 23 timesin t × n = 5 × 3 = 15 years
SME–567
COMPOUND INTEREST
7. (1) A = P 1100
+FHG
IKJ
R T
2 = 1 1100
15+
FHG
IKJ
R
Cubing on both sides, we have
8 = 1 1100
45+
FHG
IKJ
R
Required time = 45 yearsAliter : Using Rule 5,Here, m = 2, t = 15 yearsIt becomes 8 times = 23 timesin t × n years= 15 × 3 = 45 years
8. (4) A = P 1100
+FHG
IKJ
R T
Þ 24000 = 12000 1100
5+
FHG
IKJ
R
Þ 2 = 1100
5+
FHG
IKJ
R
Þ 24 = 1100
20+
FHG
IKJ
R
i.e. The sum amounts to 192000after 20 years.Aliter : Using Rule 11Here, x = 2, n1 = 5y = ?, n2 = 20
xn1
1 = y n1
215 = y
120
Þ y = 215
20FHGG
IKJJ
y = 24
y = 16 times
\ Sum = 16 × 12000
= 1,92,000
9. (1) A = P 1R
100
T+
FHG
IKJ
Þ 4 = 1R
100
2+
FHG
IKJ
Þ 1 +R
100 = 2
ÞR
100 = 1
Þ R = 100%Aliter : Using Rule 8,Here, n = 4, t = 2 years
R% = n t1
1 100%-FHGG
IKJJ ´
= 4 1 100%12b g -
LNMM
OQPP
´
= 100%
10. (2) A = P 1R
100
T+
FHG
IKJ
Let P. , A = 2
Þ 2 = 1 1R
100
3+
FHG
IKJ
On squaring both sides.
4 = 1 1R
100
6+
FHG
IKJ
\ Time = 6 yearsAliter : Using Rule 11,Here, x = 2, n1 = 3y = 4, n2 = ?
xn1
1= y n
1
2
213 =
4
1
2n
213 = 22
1
2e jn
Þ 213 =
2
2
2n
13
=2
2n
\ n2 = 6 Years
11. (2) Let the principal be 1.
\ A = P 1R
100
T+F
HGIKJ
Þ 8 = 1 1R
100
3+F
HGIKJ
Þ 23 = 1R
100
3+F
HGIKJ
Þ 2 = 1R
100
1+
FHG
IKJ
Þ 24 = 1R
100
4+
FHG
IKJ
\ Time = 4 yearsAliter : Using Rule 11,Here, x = 8, n1 = 3y = 16, n2 = ?
Usingxn
1
1= y n
1
2
813b g = 16
1
2b gn
2313e j = 24
1
2e jn
21 = 2
4
2n
Þ 1 =4
2n
n2 = 4 years
12. (3) A = P 1R
100
T+
FHG
IKJ
Let P be 1, then A = 2
Þ 2 = 1 1R
100
4+
FHG
IKJ
Þ 22 = 1R
100
8+
FHG
IKJ
\ Time = 8 yearsAliter : Using Rule 11,Here, x = 2, n1 = 4y = 4, n2 = ?
Usingxn
1
1= y n
1
2
214b g = 4
1
2b gn
214 = 22
1
2e jn
214 =
2
1
2n
Þ14
=2
2n
n2 = 8 years
SME–568
COMPOUND INTEREST
13. (3) A = PR
T
1100
+FHG
IKJ
Let P = 1, then A = 3
Þ 3 = 1 1100
3
+FHG
IKJ
R
On squaring both sides,
9 = 1 1100
6
+FHG
IKJ
R
\ Time = 6 yearsAliter : Using Rule 11,Here, x = 3, n1 = 3y = 9, n2 = ?
Using,xn
1
1= y n
1
2
( )313 = (9)
1
2n
313 = 32
1
2e jn
313 =
3
2
2n
Þ13
=2
2n
Þ n2 = 6 years14. (3) If principal = 1000, amount
= 1331
\ A = P 1100
+FHG
IKJ
R T
Þ13311000
13
= +FHG
IKJ
R100
Þ1110
13 3F
HGIKJ = +F
HGIKJ
R100
Þ 11110
+ =R
100
ÞR
100=
110
Þ R =1
10100´ = 10%
Aliter : Using Rule 8,Here, n = 1.331, t = 3 years
R% = n t1
1 100%-FHGG
IKJJ ´
= 1331 1 100%13.b g -
LNMM
OQPP
´
= [1.1 – 1] × 100%= 0.1 × 100%= 10%
15. (4) A = P 1R
100
T
+FHG
IKJ
Þ 1.44P = P 1R
100
2
+FHG
IKJ
Þ (1.2)2 = 1R
100
2
+FHG
IKJ
Þ 1R
100+ = 12.
Þ R = 0.2 × 100 = 20%Aliter : Using Rule 8,Here, n = 1.44, t = 2 years
R% = n16 1 100%-
FHGG
IKJJ ´
= 144 1 100%12.b g -
LNMM
OQPP
´
= [(1.2) – 1] × 100%= 0.2 × 100%= 20%
16. (2) A = P 1R
100
T
+FHG
IKJ
Þ278
1100
3
x x= +FHG
IKJ
R
Þ32
1100
3 3FHG
IKJ = +F
HGIKJ
R
Þ 1100
32
+ =R
ÞR
10032
112
= - =
Þ R =12
100´
\ R = 50%Aliter :
n=278
, t = 3 years
R% = n n1
1 100%-FHGG
IKJJ ´
=278
1 100%
13F
HGIKJ -
L
NMMM
O
QPPP
´
=32
1 100%FHG
IKJ -
LNM
OQP ´
= 50%
TYPE-V
1. (1) Let the rate of interest be r%per annum,According to the question,
4840 = P 1100
2+
FHG
IKJ
r..... (i)
and 5324 = P 1100
3+
FHG
IKJ
r....(ii)
On dividing equation (ii) by equa-tion (i), we have,
1 +r
10053244840
14844840
= = +
Þr
1004844840
=
Þ r = 10%Aliter : Using Rule 7 (i),Here, b – a = 3 – 2 = 1B = Rs 5,324, A = 4,840
R% =BA
-FHG
IKJ ´1 100%
=53244840
1 100%-FHG
IKJ ´
=5324 4840
4840100%
-FHG
IKJ ´
=4844840
100%´ = 10%
2. (4) Let the rate of interest = R%per annum.We know that
A = P 1100
+FHG
IKJ
R T
24202
=FHG
IKJP 1+
R100
....(i)
26623
=FHG
IKJP 1+
R100
...(ii)
Dividing equation (ii) by (i),
SME–569
COMPOUND INTEREST
126622420
+ =R
100
ÞR
100= -
26622420
1
ÞR
100=
-= =
2662 24202420
2422420
110
Þ R =1
10100 10%´ =
Aliter : Using Rule 7(i),Here, b – a = 3 – 2 = 1B = Rs. 2,662, A= Rs,2,420
R% =BA
-FHG
IKJ ´1 100%
=26622420
1 100%-FHG
IKJ ´
=2662 2420
2420100%
-LNM
OQP´
=2422420
100%´
= 10%
3. (1) A = P 1100
+FHG
IKJ
RT
\ 3840 = P 1100
4
+FHG
IKJ
R....(i)
3936 = P 1100
5
+FHG
IKJ
R...(ii)
Dividing equation (ii) by equation (i),
39363840
1100
= +R
ÞR
10039363840
1= -
=3936 3840
384096
3840-
=
Þ R =96
3840100 2 5%´ = .
Aliter : Using Rule 7(i),Here, b – a = 5 – 4 = 1B = Rs. 3,936, A = Rs. 3,840
R%=BA
-FHG
IKJ ´1 100%
=39363840
1 100%-FHG
IKJ ´
=3936 3840
3840100%
-FHG
IKJ ´
=96
3840100%´
=104
% = 2.5%
4. (4) If the principal be P, then
A = P 1100
+FHG
IKJ
rT
Þ 1440 = P 1100
2
+FHG
IKJ
r...(i)
and 1728 = P 1100
3
+FHG
IKJ
r...(ii)
On dividing equation (ii) by (i),
17281440
= 1 +r
100
\r
10017281440
1= -
=1728 1440
1440288
1440-
=
Þ r =288 100
1440´
\ r = 20% per annumAliter : Using Rule 7(i),Here, b – a = 3 – 2 = 1B = Rs 1728, A = Rs,1440
R% =BA
-FHG
IKJ ´1 100%
=17281440
1 100%-FHG
IKJ ´
=1728 1440
1440100%
-FHG
IKJ ´
=288
1440100%L
NMOQP ´ = 20%
5. (4) Difference = 238.50 – 225= 13.50= S.I. on 225 for 1 year
\ Rate =S.I. × 100
Principal × Time
=13 50 100
225 1. ´
´ = 6% per annum
Aliter : Using Rule 7(i),Here, b – a = 1
B = Rs 238.50, A = Rs,225
R% =BA
-FHG
IKJ ´1 100%
=238 50
2251 100%
.-F
HGIKJ ´
=238 50 225
225100%
. -FHG
IKJ ´
=135225
100%.L
NMOQP ´ = 6%
6. (2) A = P 1R
100
T
+FHG
IKJ
Þ 7000 P 1R
100
4
= +FHG
IKJ ....(i)
10000 P 1R
100
8
= +FHG
IKJ .......(ii)
Dividing equation (ii) by (i)
100007000
= +FHG
IKJ1
R100
4
Þ107
= +FHG
IKJ1
R100
4
From equation (i),
7000 P107
= ´
Þ P = 4900Aliter : Using Rule 7(iii),Here, b – a = 8 – 4 = 4B = Rs 10,000, A = Rs,7000
R% =BA
nFHG
IKJ -
L
NMMM
O
QPPP
´
1
1 100%
R% =100007000
1
14F
HGIKJ -
L
NMMM
O
QPPP
=107
1
14F
HGIKJ -
L
NMMM
O
QPPP
Þ 1100
+R
= 107
14F
HGIKJ
SME–570
COMPOUND INTEREST
1100
4
+FHG
IKJ
R =
107
7000 = P ×107
Q Amount = PR
1100
4
+FHG
IKJ
P = Rs. 49007. (3) Interest on 650 for 1 year
= 676 – 650 = 26
So, r = ´26650
100
Þ r = 4% per annum
PA
r t=
+LNM
OQP1
100
=
+LNM
OQP
650
14
100
1
=6502625
= ´6502526
= 625
Aliter : Using Rule 7(i),Here, b – a = 1B = Rs 676, A = 650
R% =BA
-FHG
IKJ ´1 100%
=676650
1 100%-LNM
OQP´
=676 650
650100%
-LNM
OQP ´
=26
650100%´
=10025
= 4%
Amount= PR
1100
1
+FHG
IKJ
650 = P 14
100+F
HGIKJ
Þ P =650 100
104´
= 625
Note : A sum at a rate of interestcompounded yearly becomes A,in n years and A2 in (n + 1) years,
then P AAA
n
=FHG
IKJ1
1
2
8. (1) S.I. on 2400 for 1 year= (2, 520 – 2, 400) = 120
\ Rate =´
´S I
incipal Time. .
Pr%
100
=´
´=
120 1002400 1
5%
Aliter : Using Rule 7(i),Here, b – a = 4 – 3 = 1B = Rs 2520, A = 2400
R% =BA
-FHG
IKJ ´1 100%
=25202400
1 100%-LNM
OQP´
=2520 2400
2400100%
-LNM
OQP ´
=1202400
100%´
= 5%
9. (3) Pr
1100
2
+FHG
IKJ = 4500 ...(i)
Pr
1100
4
+FHG
IKJ = 6750 .....(ii)
On dividing equation (ii) by equa-tion (i), we get
1100
67504500
2
+FHG
IKJ =
r
From equation (i),
P ´67504500
= 4500
Þ P =4500 4500
6750´
= 3,000
Aliter : Using Rule 7(ii),Here, b – a = 4 – 2 = 2B = 6750, A = 4500
R% =BA
FHG
IKJ -
L
NMMM
O
QPPP
´
12
1 100%
=67504500
1 100%
12F
HGIKJ -
L
NMMM
O
QPPP
´
=32
1 100%
12F
HGIKJ -
L
NMMM
O
QPPP
´
Þ 32
12F
HGIKJ = 1
100+
R
Þ32
= 1100
2
+FHG
IKJ
R
A = PR
1100
2
+FHG
IKJ
4500 = P ×32
P = 3000
10. (4) Principal = P (let)Rate = R% per annum
\ A = P 1R
100
T
+FHG
IKJ
Þ 650 = P 1R
100+F
HGIKJ
Þ650P
= 1R
100+F
HGIKJ ...(i)
Again, 676 = P 1R
100+F
HGIKJ2
Þ 676 = P650P
FHG
IKJ2
=P 650 650
P2´ ´
Þ P =650 650
676´
= 625
11. (2) Principal =S.I. 100
Time Rate´´
=350 100
2 4´´ = Rs. 4375
C.I. = P 1R
100–1
T
+FHG
IKJ
LNMM
OQPP
= 4375 14
1001
2
+FHG
IKJ
LNMM
OQPP–
= 4375 1125
12
+FHG
IKJ
LNMM
OQPP–
= 43752625
12F
HGIKJ
LNMM
OQPP–
= 4375676625
1–FHG
IKJ
=4375 51
625´
= Rs. 357Required difference
= Rs. (357 – 350) = Rs. 7
12. (1) Rate of interest = 12% p.a.
= 1% per month
Time = 12y months
\ A = P 1100
+FHG
IKJ
RT
Þ 64 = 1 11
100
12
+FHG
IKJ
y
Þ 64 = 1(1.01)12y
SME–571
COMPOUND INTEREST
13. (3) C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
Þ 525 = P 110
1001
2
+FHG
IKJ
LNMM
OQPP–
Þ 525 = P121100
1–FHG
IKJ
Þ 525 =P 21100´
Þ P =525 100
21´
= Rs. 2500
Again, new rate = 5% per annum
\ S.I. =Principal Time Rate
100´ ´
=2500 5 4
100´ ´
= Rs. 500
14. (2) Let the principal be Rs. x.When the interest is compound-ed annually,
C.I. = P 1R
100– 1
T
+FHG
IKJ
LNMM
OQPP
= P 120
1001
2
+FHG
IKJ
LNMM
OQPP–
= P65
12F
HGIKJ
LNMM
OQPP–
= P3625
1–FHG
IKJ = Rs.
11P25
When the interest is compound-ed half–yearly,
C.I. = P 1+10
100FHG
IKJ
LNMM
OQPP
4
1–
= P1110
14F
HGIKJ
LNMM
OQPP–
= P1464110000
1–FHG
IKJ
= Rs.4641P10000
\4641P10000
–11P25
= 723
Þ4641P – 4400P
10000 = 723
Þ241P
10000 = 723
Þ P =723 10000´
241= Rs. 30000
TYPE-VI
1. (1) A = 2550R = 4% per annumn = 2 yearsLet each of the two equal instal-ments be xPresent worth
=+F
HIK
Instalmentr n
1100
P x1 1
1 4100
=+F
HIK
=+
x
1 125
=x
2625
or P x12526
=
Similarly,
P x x2
22526
625676
= FH
IK =
P1 + P2 = A
\ + =2526
625676
2550x x
Þ( )650 625
6762550+
=x
Þ1275676
2550x =
Þ x = ´2550 6761275
x = 1352Aliter : Using Rule 9(i),Here, P = 2550, n = 2, r = 4%Each instalment
=P
r r100
100100
100
2
+FHG
IKJ +
+FHG
IKJ
=
2550
100100 4
100100 4
2
+FHG
IKJ +
+FHG
IKJ
=
2550
100104
100104
2
+ FHG
IKJ
=
2550100104
1100104
+FHG
IKJ
=
2550100104
204104
FHG
IKJ
=2550 104 104
20400´ ´
= 1352
2. (2) Using Rule 1,Let principal (present worth) forfirst year be P1 and that for twoyears be P2.
\ 16224 = P11 4
100+F
HGIKJ
Þ 16224 = +FHG
IKJ =P P
1 1 125
2625
1
Þ =´
P116224 25
26 = 15600
Again,
16224 1 41002
2= +F
HGIKJP
Þ = FHG
IKJ =16224 26
25676
6252
22P P
Þ =´
P216224 625
676= 15000
\ Cash value of the scooter= (16224 + 15600 + 15000)= 46824
3. (3) Let the annual instalment be x
A = P 1RT
T+
FHG
IKJ
x = P11
25200
+FHG
IKJ
Þ x = P198
´
Þ P1 =89
x
Similarly, P2 =6481
x
P1 + P2 = 6800
Þ 89
6481
6800x x+ =
Þ 72 64
816800
x x+=
Þ136
816800
x=
Þ x =6800 81
136´
= 4050
Aliter : Using Rule 9(i),
Here, P = 6800, R =252
%
n = 2Each instalment
=P
r r100
100100
100
2
+FHG
IKJ +
+FHG
IKJ
SME–572
COMPOUND INTEREST
=
6800
100
100252
100
100252
2
+
F
HGGG
I
KJJJ
++
F
HGGG
I
KJJJ
=
6800
200225
200225
2
+ FHG
IKJ
=
6800200225
1200225
+FHG
IKJ
=6800 225 225
200 425´ ´
´ = 4050
4. (2) Using Rule 9(i),Let each instalment be x.
\
x x
15
100 15
100
123002
+FHG
IKJ
+
+FHG
IKJ
=
Þ2021
2021
123002x
x+FHG
IKJ =
Þ2021
12021
12300x
+FHG
IKJ =
Þ2021
4121
12300x
x´ ´ =
Þ x =12300 21 21
20 41´ ´´
\ x = 66155. (2) Using Rule 9(i),
Let the value of each instalmentbe x
\ Principal = Present worth ofx due 1 year hence, presentworth of Rs. x due 2 years hence
Þ 210 =x
R1
100+F
HGIKJ
+x
R1
100
2
+FHG
IKJ
Þ 210 =x
110100
+FHG
IKJ
+x
110100
2
+FHG
IKJ
Þ 210 =x
11
10+
+x
11
10
2
+FHG
IKJ
Þ 210 =x1110
+x
1110
2FHG
IKJ
Þ 210 =1011
x +
100121
x
Þ 210 =110 100
121x x+
Þ 210 × 121 = 210 x
Þ x =210 121
210´
= 121
6. (3) Using Rule 1,Share of elder brother= Rs. x (let)
\ Share of younger brother
= Rs. (16820 – x)
A = P 1100
+FHG
IKJ
R T
According to the question,
x 15
100
13
+FHG
IKJ
= (16820 – x) 15
100
15
+FHG
IKJ
Þ x = (16820 – x) 1120
2
+FHG
IKJ
Þ x = (16820 – x)2120
2FHG
IKJ
Þ 2021
2FHG
IKJ x = 16820 – x
Þ400441
x + x = 16820
Þ400 441
441x x+
= 16820
Þ 841x = 16820 × 441
Þ x =16820 441
841´
= Rs. 8820
7. (1) Using Rule 9(i),Sum borrowed = Present worthof Rs. 17640 due 1 year hence+ Present worth of Rs. 17640due 2 years hence
= Rs.
17640
15
100
17640
15
100
2+F
HGIKJ
+
+FHG
IKJ
F
H
GGGG
I
K
JJJJ
= Rs. 1764020
2117640
20
21
20
21´ + ´ ´
FHG
IKJ
= Rs. (16800 + 16000)= Rs. 32800
8. (3) Using Rule 1,Let the amount deposited in PostOffice be Rs. x lakhs.\ Amount deposited in bank =Rs. (3 – x) lakhsAccording to the question,
x ´ ´´
10 1100 12
+( – )3 6 1
100 12x ´ ´
´
=2000
100000 =
150
Þ 10x + 18 – 6x =1
50 × 1200
= 24Þ 4x = 24 – 18 = 6
Þ x =64
= Rs.32
lakhs
\ Required difference = 09. (2) Using Rule 1,
Let the income of company in2010 be Rs. P
According to the question,
A = P 1R
100
T
+FHG
IKJ
Þ 2664000 = P 120
100
2
+FHG
IKJ
Þ 2664000 = P 115
2
+FHG
IKJ
Þ 2664000 = P65
2
´ FHG
IKJ
Þ P =2664000 5 5
6 6´ ´
´= Rs. 1850000
TYPE-VII
1. (2) Using Rule 1,
S.I.=6000 5 2´ ´
100= 600
C.I. = 5000 18
1001
2
+FHG
IKJ -
LNMM
OQPP
= FHG
IKJ -
LNMM
OQPP5000
2725
12
=-F
HGIKJ
LNM
OQP
5000729 625
625
= ´5000104625
= 832
\ Required difference= (832–600) = 232
SME–573
COMPOUND INTEREST
2. (3) Using Rule 1,Let the borrowed amount bexAccording to the question,
x x1 3100
21 4 1
100+F
HGIKJ -
LNMM
OQPP-
´ ´
= 104.50 [Q Interest is compounded half
yearly]Þ x [(1.03)2 – 1] – 0.04x= 104.50Þ 0.0609x – 0.04x = 104.50Þ 0.0209x = 104.5
Þ x =104 50 0209
..
= 5000
3. (2) Using Rule 9(i),Let each instalment be x.
x x
135400
135400
133602
+FHG
IKJ
++F
HGIKJ
=
Þ
+FHG
IKJ
++F
HGIKJ
=x x
1780
1780
133602
Þ + =64007569
8087
13360x x
Þ+
=6400 6960
756913360
x x
Þ 13360 x = 13360 × 7569Þ x = 7569
4. (3) Using Rule 1,Rate = 5%, Time= 4 half yearsP = 5000
\ C.I. = P 1100
1+FHG
IKJ -
LNMM
OQPP
RT
= 5000 15
1001
4
+FHG
IKJ -
LNMM
OQPP
= 5000194481160000
1-FHG
IKJ
=5000 34481
160000´
= 1077.5
S.I. =5000 10 2
100´ ´
= 1000
Difference = 1077.5 – 1000= 77.5
5. (2) Using Rule 3,
A = P 1100
1100
1 2+FHG
IKJ +F
HGIKJ
R RT T1 2
= 250 14
1001
8100
+FHG
IKJ +FHG
IKJ
= 250104100
108100
´ ´
\ A = 280.806. (1) Using Rule 1,
Amount given to sons
= 84100 ×12
= 42050
Amount given to B = x (let)
\ Amount given to A
= (42050 – x)
A = P 1100
+FHG
IKJ
RT
Þ (42050 – x ) 1100
3
+FHG
IKJ
R
= x 1100
5
+FHG
IKJ
R
Þ (42050 – x ) = x 1100
2
+FHG
IKJ
R
Þ (42050 – x ) = x 15
100
2
+FHG
IKJ
Þ (42050 – x ) = x 1120
2
+FHG
IKJ
Þ 42050 – x = x2120
2FHG
IKJ
Þ 42050 – x =441400
x
Þ 42050 =441400
x + x
Þ 42050 =441 400
400x x+
=841400
x
Þ 841 x = 42050 × 400
Þ x =42050 400
841´
= 20,000
7. (2) Using Rule 1,
Time =32
years
= 3 half yearsRate = 2R% per annum= R% per half year
\ Amount
= Principal – 1+Rate100
TimeFHG
IKJ
Þ 2315.25 = 2000 1100
3
+FHG
IKJ
R
Þ231525200000
= 1100
3
+FHG
IKJ
R
Þ92618000
= 1100
3
+FHG
IKJ
R
Þ2120
3FHG
IKJ = 1
100
3
+FHG
IKJ
R
Þ 1120
3
+FHG
IKJ = 1
100
3
+FHG
IKJ
R
Þ 1 +120
= 1100
+R
ÞR
100 =
120
Þ R =10020
= 5% per half year\ Required rate
= 10% per annum
8. (4) A = P 1 +FHG
IKJ
R100
n
Þ 2P = P 15
+FHG
IKJ
R100
On cubing both sides,
23 = 1+R
100FHG
IKJ
´5 3
Þ 8 = 1 1+R
100FHG
IKJ15
\ Required time = 15 yearsAliter : Using Rule 11,x = 2, n1= 5,y = 8, n2 = ?
Here,xn
1
1= y n
1
2
SME–574
COMPOUND INTEREST
215b g = 8
1
2b gn
215 = 2
3
2b gn
Þ15
=3
2n
\ n2 = 159. (4) Using Rule 1,
When the interest is payable halfyearly,= 9% per half annumTime = 4 half yearsLet the principal be Rs. P.
\ C.I. = P 1R
100–1
T
+FHG
IKJ
LNMM
OQPP
= P 19
1001
4
+FHG
IKJ
LNMM
OQPP–
= P 109 14. –b gLNM OQP= P [1.4116 – 1] = Rs. 0.4116 PAccording to the question,
= P 118100
12
+FHG
IKJ
LNMM
OQPP–
= P 118 12. –b gLNM OQP= P (1.3924 – 1) = Rs. 0.3924 PAccording to the question,0.4116P – 0.3924P = 960Þ 0.0192P = 960
Þ P =960
0 0192.
=960 10000
192´
= Rs. 5000010. (3) Using Rule 3,
Amount
= P 1R
1001+F
HGIKJ 1
R100
2+FHG
IKJ
= 25000 14
100+F
HGIKJ 1
5100
+FHG
IKJ
= 25000 ×104100
×105100
= Rs. 27300
11. (3) A = P 1R
1001+F
HGIKJ 1
R100
2+FHG
IKJ
= 10000 110
100+F
HGIKJ 1
12100
+FHG
IKJ
= 10000 ×110100
×112100
= Rs. 1232012. (1) Let the principal be Rs. P and
rate of interest be R% per an-num.
\ S.I. =Principal Time Rate
100´ ´
Þ 1400 =PR 2100
´
Þ PR = 1400 × 50= 70000 ..... (i)Again, for 2 years,
C.I. – S.I. =PR
10000
2
Þ 1449 – 1400 =PR
10000
2
Þ 49 =PR R10000
´
Þ 49 =70000 R
10000´
[From equation (i)]Þ 7R = 49
Þ R =497
= 7% per annum
13. (3) P =x1
1 + R100
+x2
21 +FHG
IKJ
R100
= Rs.
3150
15
100
4410
15
100
2+
+
+FHG
IKJ
F
H
GGGG
I
K
JJJJ
= Rs.
3150
1120
4410
1120
2+
+
+FHG
IKJ
F
H
GGGG
I
K
JJJJ
= Rs.
31502120
4410
2120
2+FHG
IKJ
F
H
GGGG
I
K
JJJJ
= Rs.3150 20
214410 400
441´
+´F
HGIKJ
= Rs. (3000 + 4000)= Rs. 7000
14. (2) Let Ram’s share be Rs. x.\ Shyam’s share= Rs. (260200 – x)
A = P 1R
100
T
+FHG
IKJ
Þ x 1R
100
4
+FHG
IKJ
= (260200 – x) 1R
100
6
+FHG
IKJ
Þ x = (260200 – x) 14
100
2
+FHG
IKJ
Þ x = (260200 – x) 1125
2
+FHG
IKJ
Þ x = (260200 – x)2625
2FHG
IKJ
Þ x = (260200 – x)676625
Þ625676
x + x = 260200
Þ625 676
676x x+
= 260200
Þ1301
676x
= 260200
Þ x =260200 676
1301´
= Rs. 13520015. (3) Interest got by A
=Principal Time Rate
100´ ´
=5000 2 6
100´ ´
= Rs. 600
C.I. received by B
' = P 1+R
100
TFHG
IKJ
LNMM
OQPP–1
= 5000 1+10100
2FHG
IKJ
LNMM
OQPP–1
= 50001110
2FHG
IKJ
LNMM
OQPP–1
= 5000121100
–1FHG
IKJ
=5000 21
100´
= Rs. 1050
\ B’s profit= Rs. (1050 – 600)= Rs. 450
SME–575
COMPOUND INTEREST
1. At what rate per annum will 32000 yield a compound interest
of 5044 in 9 months interestbeing compounded quarterly ?(1) 20% (2) 32%(3) 50% (4) 80%
2. If the difference between simpleand compound interest on someprincipal amount at 20% perannum for three years is 48,then the principal amount is:(1) 450 (2) 375(3) 390 (4) None of these
3. Find compound interest on5000 for 2 years at 10% per an-num, compounded half-yearly.(1) 1077.5 (2) 1072.5(3) 1000 (4) 1100
4. Find compound interest on
10,000 for 312 years at 10% per
annum, compounded yearly.(1) 3675.50 (2) 3775.50(3) 3875. 50 (4) 3975.50
5. Find the present worth of 9261due 3 years hence at 5% per an-num compounded yearly.(1) 8000 (2) 8200(3) 8500 (4) 8700
6. Find the ratio of simple interestto compound interest for 2 yearsat 4% per annum, compoundedyearly in case of compound in-terest.(1) 50 : 53 (2) 50 : 51
(3) 49 : 50 (4) 48 : 537. In what time will 15625 amount
to 17576 at 4% per annum, com-pounded yearly?(1) 4 years (2) 2.5 years
(3) 3 years (4) 3.5 years8. If SI on a certain sum of money
at 4% per annum for 2 years be 125, what would be the interest
if it was to be compoundedannually at the same rate and forthe same time period?(1) 127.50 (2) 125.50(3) 135.50 (4) 138
9. The compound interest on a sumof money at 5% per annum for 3years is 2522. What would bethe simple interest on this sumat the same rate and for the sameperiod ?
TEST YOURSELF(1) 2500 (2) 2400(3) 2450 (4) 2350
10. The simple interest on a certainsum for 2 years is 50 and thecompound interest is 55. Findthe rate of interest per annum andthe sum.(1) 16% P.a. ; 200(2) 15% P.a. ; 150(3) 20% P.a. ; 125
(4) 18% P.a. ; 17511. If the difference between CI and
SI on a certain sum at r% perannum for 2 years is x, findthe expression for principal sum.If the difference between CI andSI on a certain sum at 4% perannum for 2 years is 25, findthe sum.(1) 18625 (2) 16625(3) 14625 (4) 15625
12. If the difference between CI andSI on a certain sum at r% perannum for 3 years is Rs x, findthe expression for the principalsum. If the difference betweenCI and SI on a certain sum at 4%for 3 years is Rs. 608. Find thesum.(1) 125000 (2) 120000(3) 130000 (4) 122250
13. A sum amounts to 9680 in 2years and to 10648 in 3 yearscompounded annually. Find theprincipal and the rate of interestper annum.(1) 12% ; 7500(2) 10% ; 8000(3) 11% : 11000
(4) None of these14. Divide 10230 into two parts
such that the first part after 10years is equal to the second partafter 7 years, compound interestbeing 20% per annum com-pounded yearly.(1) 4150 ; 6080(2) 3950 ; 6280(3) 3750 ; 6480(4) 3550 ; 6680
15. A sum of 1682 is to be dividedbetween A and B who are respec-tively 20 years and 22 years old.They invest their shares at 5%per annum, compounded annu-ally. At the age of 25 years both
receive equal amounts. Find theshare of each.(1) 730 ; 952(2) 750 ; 932(3) 700 ; 982(4) 800 ; 882
16. A sum of money was lent at 10%per annum, compounded annu-ally, for 2 years. If the interestwas compounded half-yearly, hewould have received 220.25more. Find the sum.(1) 40000 (2) 45000(3) 48000 (4) 50000
17. Ram invests 5000 in a bondwhich gives interest at 4% perannum during the first year, 5%during the second year and 10%during the third year. How muchdoes he get at the end of thirdyear ?(1) 7000 (2) 5006(3) 6006 (4) 5506
SHORT ANSWERS
1. (1) 2. (2) 3. (1) 4. (4)
5. (1) 6. (2) 7. (3) 8. (1)
9. (2) 10. (3) 11. (4) 12. (1)
13. (2) 14. (3) 15. (4) 16. (1)
17. (3)
EXPLANATIONS
1. (1) Using Rule 1,Let the rate of CI be R per centper annum.
\ CI = +FHG
IKJ -
LNMM
OQPPP 1 R
1001
T
Þ 5044
= 32000 1R
4001
3
+FHG
IKJ -
LNMM
OQPP
[Q Interest is compounded quar--terly]
Þ = +FHG
IKJ -
504432000
1 R400
13
Þ +FHG
IKJ -1 R
4001 = 1261
8000
3
SME–576
COMPOUND INTEREST
Þ +FHG
IKJ =1 R
4001 + 1261
8000
3
Þ +FHG
IKJ = = F
HGIKJ1 R
40092618000
3 2120
3
Þ + = Þ = - =1 R400
R400
2120
2120
1 120
Þ = =R 40020
20 % per annum
2. (2) Using Rule 6,
P =D 1003
2´
+r r 300b g
=´
+48 1003
400 20 300b g = Rs. 375
3. (1) Using Rule 1,
A = +FH IKP r t1 200
2
Here, P = 5000r = 10% per annumt = 2 years
So, A = +FHG
IKJ5000 1 10
200
4
= +FH
IK5000 1
5100
4
= ´5000 194481160000
=194481
32A = 6077.5CI = (6077.5 – 5000)= 1077.5.
4. (4) Using Rule 4,
A = +FH IK +F
HGG
I
KJJP r
r1 100 1 2
1003
= +FH
IK +FH
IK10 000 1
10100
15
100
3,
= ´ ´10 000 13311000
2120
,
A = 13975.5CI = (13975.5 – 10,000)CI = 3975.5.
5. (1) Using Rule 1,
P =+FH IK
Ar t
1 100Here, A = 9261r = 5% per annumt = 3 years
P =+FH IK9261
1 5100
3 =926192618000
P = 8000.
6. (2)SICI
=
+FH IKLNMM
OQPP
rtr t
100 1 100 1–
=´
+FH
IK
LNMM
OQPP
4 2
100 1 4100
12
–
= FH
IK
2
25 676625
1– =´´
2 62525 51
SICI
= 5051 = 50 : 51
7. (3) Using Rule 1,A = 17576P = 15625r = 4% per annum
A = +FH IKP r t1 100
1 100+FH IKr t
= AP
1 4100+FH IK
t= 17576
15625
2625
FH IKt
= 1757615625
=2625
3FHG
IKJ
\ t = 3 years.
8. (1)CISI =
+FH IKLNMM
OQPP
100 1 100 1r
rt
t–
=
+FH
IK
LNMM
OQPP
´
100 1 4100
1
4 2
2–
=´ FH
IK
´
100 676625
1
4 2
–
CI125
= ´´ ´100 51
4 2 625
CI =100 51 125
4 2 625´ ´
´ ´CI = 127.5.
9. (2)
SI = ´
+FHG
IKJ
LNMM
OQPP
CI rt
r t100 1
1001–
=´ ´
+FH
IK
LNMM
OQPP
2522 5 3
100 1 5100
13
–
SI =´ ´
9LNM
OQP
2522 5 3
100 2618000
1–
=´ ´
´´
2522 5 3100 1261
8000
SI = 2400.10. (3) The difference between CI
and SI for 2 years period is be-cause CI also includes interest forthe second year on the first year’sinterest.CI – SI = (55 – 50) = 5
First year’s SI =502
= 25
So, 5 is the interest on 25 for1 year.
r =100 I
ptHere, I = 5P = 25t = 1 year
\ r = ´´
100 525 1
r = 20% per annum.
Now, P =100 I
rtHere, I = 50r = 20% per annumt = 2 years.
P = ´´
100 5020 2
P = 125.Note : Derivation for 2 yearsproblems :
Rate =´
´2
100CI SISI
–b g
Sum =´
´SI 100
2Rate11. (4) Let the sum be P
SI =´
=P Prr 2100
2100
SME–577
COMPOUND INTEREST
CI = +FH IKLNMM
OQPPP r1 100 1
2–
= + +LNMM
OQPPP
r r1
100
2100
12
2( )–
CI = +LNM
OQP
P r r2
21002
100
CI SI– = +LNM
OQP
P r r Pr2
21002
1002100
–
Let, CI – SI = x
x =Pr2
1002 P = xr
100 2FHG
IKJ
Here, x = 25r = 4% per annum
P = FH IK25 1004
2
P = 25× 625P = 15625.
12. (1) Using Rule 6,Let the sum be P
SI =´
=Pr Pr3100
3100
CI = +FH IKLNMM
OQPPP r1 100 1
3–
CI = + + +LNM
OQP
P r r r1100
3100
3100 1
3
3
2
2 –
CI = + +LNMM
OQPP
P r r r3
3
2
21003
1003
100Þ CI – SI (x ) =
= + +LNM
OQP
P r r r Pr3
3
2
21003
1003
1003100
–
x = +LNM
OQP
P r r3
3
2
21003
100
x =FHG
IKJ +P r r
2
3100300
P xr r
=+
100300
3
2a fa f
Here, x = 608 (given) andr = 4% per annum
P = ´ ´ ´´ ´ +
608 100 100 1004 4 4 300b g
P = Rs. 1,25,000.
13. (2) Using Rule 1,Let P = xr = r% p.a.A1 = 9680t1 = 2 yearsA2 = 10648t2 = 3 yearsInterest on 9680 for 1 year= 10648 – 9680 = 968
\ r =´968 100
9680 = 10%
Using A = P r t
1+FHG
IKJ100 we get
9680 = x x1+FHG
IKJ = F
HGIKJ
10100
1110
2 2
Þ x = 9680 ×1011
1011
8000´ =
\ Principal = 8000.14. (3) Using Rule 1,
Let the first part be x and thesecond part y.The first part after 10 years
= +LNM
OQPx 1 20
10010
The second part after 7 years
= +LNM
OQPy 1 20
1007
As given in the problem these twoamounts are equal.So,
y 1 20100
7+FH IK = +FH IKx 1 20
100
10
oryx = +FH IK1 20
100
3
oryx = 216
125and we have y + x = 10230Using the ratio formula
y =+
´216
216 12510230 = 6480
x =+
´125
216 12510230 = 3750
15. (4) Using Rule 1,For A, time = 5 yearsFor B, time = 3 yearsr = 5% per annum
A 1 5100
5+FH IK = +FH IKB 1 5
100
3
BA = +FH IK1 5
100
2
BA
= 441400
As given, A + B = 1682
So, A =+
´400
400 4411682
= 800
and B =+
´441
400 4411682
= 88216. (1) Using Rule 1,
Let the sum be P.When compounded yearly,amount
= +LNM
OQP =P P1 10
100121100
2
When compounded half-yearly,amount
= +LNM
OQP =P P1 5
100194481160000
4
So,194481160000
121100
–LNM
OQP P = 220 25.
(Given difference)
or 194481 193600160000
– P = 220 25.
or881
160000P = 220.25
or P = ´160000881 220 25.
or P = 40,000.17. (3) Using Rule 3,
A= +FHG
IKJ +FHG
IKJ +FHG
IKJP
r r r1
1001
1001
1001 2 3
Here, P = 5000r17 = 4%r2 = 5%r3 = 10%
A = +FH IK +FH IK +FH IK5000 1 4100 1 5
100 1 10100
= ´2
´ ´5000 625
2120
1110
A = 6006.